





> oy 


a, 











( ——THE SCHOOL BULLETIN PUBLICATIO 


Teachers’ Question Books. 


The increasing severity of examinations for licenses to teach, and partic- 
ularly the frequent addition of new subjects to the list upon which examina- 
tion is held has made books of Examination Questions almost essential to 
the teacher, that he may test himself in private before submitting to a pub- 
lic ordeal.. The best of these are the following. 











1. The Regents’ Questions in Arithmetic, Geography, Grammar and Spell- 
ing from the first examination in 1866 to June 1882 2. Being the 11,000 Questions 
for the preliminary examinations for admission to the University of the 
State of New York, prepared by the Regents of the University, and partici- 
pated in simultaneously by more than 250 academies, forming a basis for the 
distribution of more than a million of dollars. Complete with Key. Cloth, 
1dmo, pp. 473. $2.00. 

2.. Complete. The same as above but without answers. Pp. 340. $1.00. 

In the subjects named, no other Question Book can compare with this 
either in completeness, in excellence, orin popularity. By Legislative Enact- _ 
ment no lawyer can be admitted to the bar inthe State of New York without 
passing a Regents’ Examination in these subjects. 


3. The Dime Question Books, with full answers, notes, queries, etc. Paper, 
pp. about 40. Each 10 ets. 


Elementary Series. Advanced Series. 
3 Physiology. 1. Physics. 
, 4, Theory and Practice. 2. General Literature, 
6. U.S. History and Civil Gov’t. 5. General History. 
10. Algebra. 7. Astronomy. 
13. American Literature. 8. Mythology. 
14, Grammar. 9. Rhetoric. ; 
15. Orthography and Etymology. 11. Botany. ee . 
18. Arithnfetic. 12. Zodlogy. Of i 
19. Physical and Political Geog. 16. Chemistry, 
20. Reading and Punctuation. ; 7. Geology Dae 
Hutra Volume, 21. Temperance Physloloer. k 


~ The immense sale of the Regents’ Questions in Arithmetic, Geography, 
Grammar, and Spelling has led to frequent inquiry for similiar questions in 
advanced ‘subjee ts. To meet this demand, we have had prepared this series 
of Question Books, by which the teacher need purchase books only on the — 
subjects upon which special help is needed. Frequently a $1.50 book is — 
bought for the sake of a few questions in a single study. Here, the studies 
may be taken up one at a time, a special advantage in New York, since appli- — oa 
cants for State Certificates may now present themselves Jor examination in only 
part of the subjects, and receive partial Certificates to be exchanged for full, Cer-— 
’ tificates when all the branches have been passed. The same plan is very gener-— 
ally pursued by county superintendents and commissioners who are encour-_ 


ing their teachers to prepare themselves for higher certificates. J 
4. The ah School Question Book. By- Asa L. Crate. Cloth, 12 mo., ; 
pp. 340. $1.50 v8 







“The sale of this book continues marvellous. There is probably no coun a. 
in the United States where copies may not be found. Wegiveitnowa mi 
handsomer binding than heretofore. 
5. New York State Examination Questions., Cloth, 16mo, pp. 180. 50 ae rade i 
This contains all the questions given at all the New York Examinations 
for State Certificates from the beginning. There are more questions andin 
greater variety than in any other collection. It does not give answers. | = 
C. W. BARDEEN, Publisher, Syracuse, N. Y. | 
\ i re 4 





R 


BEING TI 


UNIV 





= THE 


NOTICE: Return or renew all Library Materials! The Minimum Fee for 
each Lost Book is $50.00. 


The person charging this material is responsible for 
its return to the library from which it was withdrawn 
on or before the Latest Date stamped below. 


Theft, mutilation, and underlining of books are reasons for discipli- 
nary action and may result in dismissal from the University. 
To renew call Telephone Center, 333-8400 


UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN 





L161—O-1096 


aN 





___THH SCHOOL BULLETIN PUBLICATIONS,—— he ee 


Teachers’ Question Books. 


The increasing severity of examinations for licenses to teach, and partie- 
ularly the frequent addition of new subjects to the list upon which examina- 
tion is held has made books of Examination Questions almost essential to 
the teacher, that he may test himself in private before submitting to a pub- 
lic ordeal.: The best of these are the following. . 








—_———- 


1, The Regents’ Questions in Arithmetic, Geography, Grammar and Spell- 
ing from the first examination in 1866 to June 1882. Being the 11,000 Questions 
for the preliminary examinations for admission to the University of the 
State of New York, prepared by the Regents of the University, and partici- 
pated in simultaneously by more than 250 academies, forming a basis for the 
distribution of more than a million of dollars. Complete with Key. Cloth, 
16mo, pp. 473. $2.00. 

2.. Complete. The same as above but without answers. Pp. 340. $1.00, 

In the subjects named, no other Question Book can compare with this 
either in completeness, in excellence, orin popularity. By Legislative Enact- 
ment no lawyer can be admitted to the bar inthe State of New York without 
passing a Regents’ Examination in these subjects. 


3. The Dime Question Books, with full answers, notes, queries, etc. Paper, ; 
Ppp. about 40. Each 10 ets. : 


Elementary Series. Advanced Series. 

3 Physiology. 1. Physics. 

, 4, Theory and Practice. ~ 2. General Literature, 
6. U.S. History and Civil Goy’t. 5. General History. 
10, Algebra. 7. Astronomy. 
13. American Literature. 8. Mythology. a 
14. Grammar. 9. Rhetoric. 2 j 
15. Orthography and Etymology. 11. Botany. - ; 4 
18. Arithnietic. 12. Zodlogy. it 
19. Physical and Political Geog. . 16. Chemistry. 
20. Reading and Punctuation. L 17. Geology. 


Hutra Volume, 21. Temperance Physiology. 


' The immense sale of the Regents’ Questions in Arithmetic, Geography, 
Grammar, and Spelling has led to frequent inquiry for similiar questions 
advanced subjects. To meet this demand, we have had prepared this series 
of Question Books, by which the teacher need purchase books only on the — 
subjects upon which special help is needed. Frequently a $1.50 book is 
bought for the sake of a few questions in a single study. Here, the studies — 
may be taken up one at a time, a special advantage in New York, since appli- 
cants for State Certificates may now present themselves for examination in only — 
part of the subjects, and receive partial Certificates to be exchanged for full Cer-— 

 tificates when all the branches have been passed. The same plan is very gener- — 
ally pursued by county superintendents and commissioners who are encour= — 














ing their teachers to prepare themselves for higher certificates. Benet 
kh, The Common School Question Book. By Asa L. Crate. Cloth, 12 mo, : 


pp. 340. $1.50 cee g 
-The sale of this book continues marvellous. There is probably no county _ 

in the United States where copies may not be found. Wegiveitnowamue “4 

handsomer binding than heretofore. - 
5. New York State Examination Questions, Cloth, 16mo, pp. 180. 50 hal ; 


This contains all the questions given at all the New York Examinations 
for State Certificates from the beginning. There are more questions and in 
greater variety than in any other collection. It does not give answers. ent 


C. W. BARDEEN, Publisher, Syracuse, N. Y. 


Px: 





REGENTS’ QUESTIONS 


FROM THE FIRST EXAMINATION IN 1866 
TO. 1882, 


BEING THE 5500 QUESTIONS FOR THE FIRST 48 PRELIMINARY EXAMINATIONS 
FOR ADMISSION TO THE: 


UNIVERSITY OF THE STATE OF NEW YORK 
a PREPARED BY THE 
REGENTS OF THE UNIVERSITY, 


-{D PARTICIPATED IN SIMULTANEOUSLY BY NEARLY TWO HUN- 
DRED AND FIFTY ACADEMIES, FORMING A BASIS FOR 
DISTRIBUTING MORE THAN A MILLJON OF DOLLARS. . 


COMPILED BY 


DANIEL J. PRATT, A.M., Px.D., 


ASSISTANT SECRETARY, REGENTS OF THE UNIVERSITY. 


{ Part I. ARITHMETIC. 


UNIVERSITY Qi} 
ILLINOIS. LIBRARY 
\URBANA-CHAMPAIGN 


AATLIEC 


WIAA E IL! -MATICS 





SYRACUSE, N. Y.: 
Cc, W. BARDEEN, PUBLISHER, 
SAN 1887. | 


COPYRIGHT, 1877, 1880, 1886, By C. W. BARDEEN. 


DATES OF THE EXAMINATIONS IN 
ARITHMETIC. 


The fifty examinations in Arithmetic are numbered, 


and the date upon which each was held will be found in 
‘the following table, opposite the corresponding number. 


Om AnDoh WMH 


. Noy. 8, 1866. 
. March 1, 1867. 
. dune 14, 


Nov. 8. 


. Feb. 21, 1868. 


dune 5. 
Novy. 13. 


. Feb. 19, 1869. 
. dune 11. 

10. 
gas 
12. 
13. 
14, 
15. 
16. 
INE 


Nov. 11. 
Feb. 11, 1870 
June 9. 
Noy. 11. 


‘Feb. 23, 1871. 


June 8. 
Nov. 9. 
Feb. 27, 1872. 


18. 
19. 
20. 
21. 
22. 
23. 
24, 
25. 
26. 


June 6, 1872. 
Nov. 7. 


Feb. 27, 1873. 


June 5. 
Nov. 6. 


Feb. 26, 1874. 


June 4, 
Nov. 5. 


Feb. 25, 1875. 
. dune 3. 
. Nov. 4. 
. Feb. 24, 1876. 
. June 8. 
. Noy. 9. 
. March 1, 1877. 
. June 7. 
. Noy. 8. 


SB8&a5 


SaPASBAS SSSR 


. Feb. 28, 1878. 
. dune 6. 


Nov. 7 
Feb. 27, 1879. 
dune 5. 
Noy. 6. 


. Feb. 26, 1880. 
. dune 3. 


June 17.* 


. Noy. 11. 

. March 3, 1881. 
. March 25.* 

. dune 16. 


Nov. 17. 


. March 2, 1882. 
. dune 15. 


*Substitute examination, protest having been made against the difficul- 
ty of the preceding one. 


UniVERSITY OF iLLINOIS 
Pedagogical Library & Mugeurn. 


ri 


oe Ye 
Ahn 3 fv 


ARITHMETIC. | 





pay (palo ch 


1. Write in figures each of the following numbers, 
add them, and express in words (or numerate) their 
sum: fifty-six thousand, and fourteen thousandths; 
nineteen, and nineteen hundredths; fifty-seven, and 
forty-eight ten-thousandths; twenty-three thousand five, 
and four tenths, and fourteen millionths. 

2. What is the difference between 3? plus 73, and-4 
plus 23? 

3. In multiplying by more than one figure, where is 
the first figure in each partial product written, and why 
is it so written? . 

4. If the divisor is 19, the quotient 37, and the re- 
mainder 11, what is the dividend? 

5. What is the quotient of 65 bu. 1 pk. 3 qt. divided 
by 12? | 

6. Which one of the fundamental operations (or ° 
ground rules) of arithmetic is employed in reduction 
descending? Give an example. 

7. In exchanging gold dust for cotton, by what 
weight would each be weighed? 

8. What is the only even prime number? 

9. How many weeks in 8,568,456 minutes? 

10. To what ¢erm :in-division does the value of a 
common fraction correspond? 


Py Sead 


6 THE REGENTS’ QUESTIONS. 


38. Find the value of the omitted term in the follow- 
ing proportion :— 

S420) e007 1G, 

39. If 56 tbh. of butter cost $15.68, what will .078 of 
a ton cost? 

40. If 96 horses eat 192 tons of hay in one winter, 
how many tons will 150 horses eat in 6 winters? 

41. In one yr. 4 mo., $311.50 amounted to $336.42 at. 
simple interest: what was the rate per cent? 

42. What is the interest of $14,231.50 from June 29, 
1860, to April 30, 1865, at 84 per cent? 

43. Three notes are payable as follows:—one for $200, 
due January 1, 1866; another for $350, due September 
1, 1866; a third for $500, due April 1, 1867: what. 
-is the average of maturity, or the equated time of pay- 
ment? 

44, How much will it cost to carpet a parlor 18 feet: 
square, with carpeting ¢ yd. wide, at $1.50 per yd.? 

45. The difference in the local time of two places is 2: 
hr. 18 m.: what is the difference in longitude? 

46. 33 is 23 per cent. of what number? 

47. What is the length of each side of a square field 
which contains 5 acres? 

48. A note for $470.66 drawn at 60 days, is discount- 
ed at bank at 6 per cent.: what are the proceeds? 


ee ee 


49, Express in figures MDXXVCODLXXXIX. 

50. Perform the operations indicated as follows:— 
102 — 19 x 17 plus 205 +3 =? 

51. Numerate (or express in words) 90067236708. 


ARITHMETIC, ‘g 


52. What is the sum of 3912, 361, 40005, 98, 736863, 
8342, 2900687, 9, 4000862, 28? 

53. If two persons start from the same place, and 
travel in the same direction, one 7 and the other 11 
miles per hour, at the rate of 9 hours per day, how far 
. apart will they be at the end of the 17th day? 

54. What is the amount due on the following bill of 
parcels: 

ALBANY, June 1, 1866. 

JOHN BARNES, 

Bought of NATHAN HADLEY & Co., 
16 tb. tea, @ 1.05 - - - $ 
18 ib. sugar, @ .14 - - ~ - 


25 th. rice, @ .09 - 2 2 
15 yd. linen, @ .66 - : 2 





Or. $ 
By balance of account, - - - - 2.48 
Balance due, - - - $ 


Received eniene N. Hapitey & Co. 


55. State the process of reducing inches to leagues. 

56. How many bu. will a box 8 ft. long, 4 ft. wide, 
and 3 ft. nee contain ? 

57. Add 36, # and =44. 

58. Brice 1943 to Re lowest terms. 

59. Give the rule for reducing fractions having differ- 
ent denominators to equivalent fractions having the 
least common denominator. 

60. Multiply 18% by 74. 

61. Express in figures, forty-seven, and twenty-one 
hundred-thousandths. 

“62. Divide 2019.86928 by 30s4,. 


8 THE REGENTS’ QUESTIONS. 


63. If 9 men cut 150 acres of grass in 18 days, how 
many will do the same work in 27 days? 

64. If 500 copies of a book containing 210 pages re- 
quire 12 reams of paper, how much will 1,200 copies of 
a book of 280 pages require? ; 

65. What is the value in currency of $865 in gold, 
when the latter is selling at 131 per cent? 

66. What is the interest on $200 for three years and 
ten months, at 7 per cent? 

67. In what time will a sum of money double itself 
at an annual interest of 5 per cent? 

68. What is the face of a note at 30 days, which yields 
$500 when discounted at bank, at 7 per cent? 

70. Extract the square root of .0043046721. 

71. Involve 1.06 to the 4th power. 

72. What debt can be discharged in a year by weekly 
payments in arithmetical progression, the first being 
$24, and the last $1,224? 


gerd eo 


73. Express in words 2584503962047. 

74, 2468113579+100+6042+187+19= 

75. What is the difference between 576—208+1645 — 
3821, and 403 —256-+814—195? 
%6. Multiply forty-nine million forty thousand six 
hundred and ninety-seven, Py nine million for ty thous- 


and seven hundred and nine 4y YS /) 6/0/43 9) / 
77. One factor of a certain ‘number is 11, I the 
other 3708311605: what is that number? * 9 ~~» aT ts 


78. If the remainder is 17, the quotient 610, aa the 
dividend 45767, what is the divisor? 


ARITHMETIC. 9 


79. What cost 3 A. 2 R. 20rd. of land, at $43 per 
acre? P/GS-£ 7S 

~80. What is the difference of time gue July 15, 
1857, and April 25, 1862? “_ 


es cwt. qr. ib. OZ. dr. 
14 13 2 15 15 15 
13 1 3 13 11 13 
81. Add 46 16 3 11 13 10 
14 15 2 7 6 9 
11 Le 3 10 15 11 





FOROS gs Fi 
82. Find the greatest common divisor of 492, 44 
and 1044, -2%2x35 /¢ 
83. Divide 137 fb. 9 oz. 18 Bae 22 gr. by 23. 
84. From # of 137 subtract. 4 of 317. 
85. Write eleven thousand, ang eleven hundred-thous- 
andths, (the whole as a single expression. ) 
86. Multiply .0097 by .000125. 
87. Divide 475 by 1283. 
88. What cost 14 of an acre at $1.75 per sq. rod? 
89. Divide 9811.0047 by .325947. 
90. Reduce 18s. 3¢d. to the decimal of a £. 
91. Find the third term of 7: 8::(?) : 12. 
92. If 24 yd. of broadcloth cost $18, what will 27 yd. 
cost? : 
93. If 8 men spend $64 in 13 weeks, what will 12 
men spend in 52 weeks? 7? © ° 
94, Find the interest on $35.61 from Nov. 11, 1857 to 
Dec. 15, 1859, at 6 per cent? 7° % - 
95. What is the bank discount on a note for $350, — 
payable 3 months after date, at 7 per cent. interest? | 
96. Find the square root of .876096. © 


10 THE REGENTS’ QUESTIONS. 
28 be a 


97. Add together 15262986957 and 3879, and multi- 
ply the 19th part of the sum by 76. 

98. Subtract nine hundred and fourteen thousand 
nine hundred and twenty, from four hundred millions 
and thirteen thousand. 

99. A wheel makes 880 revolutions in passing over 2 
mi. 1,430 yd.: what is its circumference? 

100. Reduce 49 wk. 6 da. 19 hr. to minutes. 

101. Find the greatest common divisor of 4004 and 
5772. 

102. Find the least common multiple of 25, 36, 33, 
12, 45. 

103. Divide 52 yd. 1 ft. 103 in. by 344. 

104. Reduce 3$ of 1,4, of 2,5, to a decimal. 

105. Find the value of 169 multiplied by .0000728. 

106. Find the value of 25.000315—.0045 plus .2801 
minus 18 plus 21.001. 

107. Divide the number 54 into 3 parts, proportioned 
as 2, 3, 4. - 

108. If for a certain sum 18 sheep may be grazed 20 
days, how many days may 30 sheep be grazed for the 
same sum? 

109. How many acres could 10 men plow in 14 hours, 
if 5 men plow 6 acres in 104 hours? 

110. Standard silver is composed of 37 parts of pure 
silver, and 3 parts of copper: how much per cent of 
the whole is each of the components? 

111. If I buy cloth at $1.20 per yard, how must, I 
sell it so as to gain 25 per cent? 

112. Divide $1,200 between A. and B. so that A.’s: 
share may be to B.’s as 2 to 7. 


td 


ARITHMETIC, ics 


113. Divide 6s. 6d. between Jane and Ellen, so that 
Jane may receive 3s. more than Ellen. 

114. What is the value of the square root of 4224 
X28? 

115. How much coffee at 9, 11 and 14 cents a pound, 
will form a mixture worth 12 cents a pound? 

116. When the extremes and the number of terms in 
an arithmetical series are given, how is the sum of the 
series ascertained? 

117. The surface of a square table is 26 sq. feet, 100 
in.: find the length of each side. 

118. How many square yards of matting would cover 
a floor, the dimensions of which are 20 ft. 10 in., by 
15 ft. 54 in.? 

119. What sum of money will in 3 years, 10 mo. and 
9 days at 7 per cent. amount to $1,524.10? 

120. I have three notes payable as follows: one for 
$200, due Jan. 1, 1869; another for $350, due Sept. 1, 
1869; and another for $500, due April 1, 1870; what is 
the average of maturity? 


a faa 


121. Express in figures the number represented by 
four units of the tenth order, six of the eighth, four of 
the seventh, two of the sixth, one of the third, and five 
of the second. 

122.. Numerate the expression obtained in the answer 
to Q. 121. 

(123. How may 25,000 be expressed in Roman nu- 
merals? 

124. How is the local value of a figure determined, or 
upon what does it depend? 


12 THE REGENTS QUESTIONS. 


125. What is the sum of the composite numbers from 
50 to 80 inclusive? 

126. From sixty-five trillion three million six hun- 
dred and twelve, take nine billion one million ae 
thousand and six. 

127. A tax of thirty million fifty-six Enoueattl four 
hundred and sixty-five dollars is assessed equally on four 
thousand and ninety-seven towns: what sum must each 
town pay? 

128. Which of the fundamental rules is employed in 
reducing a denominate fraction to integers of lower de- 
nominations? 

129. How many cubic inches does the standard unit 
of liquid measure contain? | 

130. How many cords of wood in a pile 140 ft. long, 
44 ft. wide, and 64 ft. high? 

131. A stationer bought 1 great gross of slates at 
9 pence each; what was the whole cost, in pounds 
sterling? 

132. Of what factors of two or more numbers does 
their greatest common divisor consist? 

133. What is the smallest sum of money with which 
horses can be bought at $50 each, cows at $30 each, 
or sheep at $8 each, using the same amount in each 
case? 

134. Express in words 0.500072. 

135. What number must be multiplied by 15% that 
the product may be 563? 

136. How is the value of a fraction affected when its 
denominator is divided by a number greater than unity? 

137. How do you multiply .061 by 100,000? 

138. What amount is due on the following items?: 


* ARITHMETIC. 13 


37 chests green tea at $ 23 75 each. 
aoe eblack.* oe Lele. 
12 crates Liverpool ware ‘“‘ 17500 “ 
19 bbl. Genesee flour eae Ler re 
23 bu. rye SOT MIRIG EIT &F 
$ 
139. When are four quantities said to be in pro- 
portion? | 
140. If ¢ of the distance from A to B is 32 miles, 
what is 3; of the same distance? 
141. How is the rate per cent ascertained when the 
principal, interest, and time are given. 
142. If $300 gain $18 in nine months, what is the 
per cent? 5 
143. What is the length, in feet and inches, of each, 
side of a square carpet, made from 494 yd. of Brussels 
carpeting, } yd. wide? 
144. How is the last term of a geometrical series 
found, the first term, ratio, and number of terms being 
given? 





4 


jE a alk 


145. Express in figures six hundred million seventeen 
thousand three hundred and eight. 

146. What is the sum of 372856, 404932, 2704793, 
9078961, 304165, 207708, 41274, 375, 271, 34 and 6? 

147. From sixty-five billion three million six hun- 
dred and twelve, take nine billion one million four 
thousand and six. 4 
- 148. One factor of a certain number is 11, and the 
other 3708311605: what is that number? ee 
- 149. What are the prime factors of 800? ire 


14 THE REGENTS’ QUESTIONS. 


150. If the quotient is aoe eae the divisor 281, what 
is the dividend? / 2 é é 

151. If I take 18729 ine the sum of 8762 and 14967, 
divide the remainder by 50, and multiply the i 2 
by 19, what is the product? & 0 

152. How many miles in 60,750 links? o2 

153. What is the sum of 4 of 93, and J oof 328324422" 

154. Reduce $ of 44 of 64 of 17 to a simple fraction. 

155. How many times is § contained in 837?)4 06 2 

156. Reduce ;%; of an acre to lower donominsa aie qe 

157. Find the greatest common divisor of 492, 744, 906. | 

158. What is ans least common multiple (or dividend} — 
of the nine digits? 2? ¢ : 

159. Divide 0.01764144 by 0. 0.0018. | 

160. Reduce 7 fur. 29 rd. to the asin of a mile.’ 

161. What sum, at 7 per cent, will amount to $221- 

.075 in 3 years 4 months? - 

162. What is the amount of $1, 200 for 2 year iF 6 
per cent compound interest, payable quarterly? ’% 

163. If $100 gain $6 in 1 year, what principal will 
gain $12 in 8 months? | 
_ 164. To what number has } the same ratio as exists 

between 3 and 21? © 

165. What number of men will be required to perform 
a ane of work in 8 ieeghee that would take 15 men 24 
da 

166. A. and B. onder inet partnership. A. furnishes 
$240 for 8 months; and B. $560 for 5 months, They 
lose $118. How ar does each lose? 4 , D 

167. What is the square root of 61723020.96? 

168. How many cubic quarter-inches are contained in 
a cubic inch? 


ARITHMETIC, 15 


8 








169. Add the following numbers: One hundred and 
eight. billion three hundred and six; twenty-one bil- 
lion twenty thousand two hundred and ten; thirty 
billion twenty-nine million and three. / 5 2 

170. Reduce 2,579, 092 drams avoirdupois to higher 
denominations. 

171. Reduce 1 mi. 18 a 2 yd. 2 ft. to inches. 

ATR. ae ee % of 12 by 33+16. 

173. Divide 33; of $4 by 4. 

174. Find the ed common multiple of all the even 
numbers from 1 to 15. 

175. From the sum of $ and 4 take 45. 

_ 176. Add together 7,55 hhd. aria 2 oil. , 
177%. Multiply 30.6002 by two and one ielehOeean den. C/ 
178. Divide 4.08 by .000136. © 
179. Reduce 348 to a decimal. | 
180. Reduce 8 oz. 5 pwt. 3 gr. to the decimal of a ib. 
181. If 21 men in 12 days can do certain work, how 

many men in 7 days could do as much? 2 & « 

182. How much will it cost to dig a cellar 40 ft. Taig. 
82 ft. wide, and 5 ft. deep, at $0.25 a cubic yard? 

183. A. begins business with $500; at the end of 2 
months B. puts in $300; at the end of 1 month more C. 
puts in $600; at the end of 5 months more the profits 
amount to $1,056. What is each man’s share? 

184. 3 pence is what per cent of 4 shillings? 

185. What sum in 1 year will yield $48.75 at 124 per 

cent? 

186. What is the bank discount on a note for $600 for 
2 months and 9 days, at 10 per cent per annum? 


16 THE REGENTS’ QUESTIONS. 


187. I sell goods for $511.29 and gain 9} per cent: 
what did the goods cost me? 

188. At what rate will $500 yield $34 interest in 1 
year, 1 month, and 18 days? 

189. What is the compound interest of $200 for 3 
years at 7 per cent? 

190. How much gold will $100 currency buy, gold 
being at 147? 

191. What is the square root of 403.6081? 

192. What is the cube root of 19$1208? 


Lphigaon 3 


193. The factors of a number are three hundred 
ninety-seven thousand five hundred, and nine thousand 
eight hundred. What is the product expressed in 
words? 

194. If one man can mow 1.875 acres in a day, how 
many acres can 13 men mow in 7.5 days? 

195. How many reams of commercial note paper each 
8 in. long, 5 in. wide, and 3.5 in. thick, can be packed 
in a box, the inside dimensions of which are 4, 14, and 
zz feet respectively? 

“196. A note given May 10, 1867, was paid August 10, 
1868. How long did the note run? 

196a. How long is a field containing 14 A., if it is 35 
rd. wide? 

19%. If I start from latitude 15° 35’ 40” north, and 
travel due north 2,159 geographic miles, in what latitude 
shall I then be? 

198. How many seconds in the circumference of a 
circle? 


~ ARITHMETIC. 17 


199. Is 217 a prime or a composite number? 

200. The four sides of my garden are 168 ft., 280 ft., 
182 ft., and 252 ft. respectively: what is the greatest 
length of boards that I can use in fencing it, without 
cutting any of them? 

201. What is the smallest sum of money for which a 
person can purchase oxen at $85 each, or cows at $35 
each? 

202. The tide rose 2 ft. one hour, 13 ft. the next, 
and # ft. the third hour: how much did it rise in the 
three hours? 

203. How many square rods are there in a lot 154 
rods long and 12 rods wide? 

204. If 8% qt. of strawberries cost $32 what is the 
price per qt.? 

205. The product of three factors is 194, and two of 
them are 14 and 22; what is the other? 

206. Reduce 4 da. 4 hr. 48m. to the decimal of a 
week. 

207. If 5 tons of coal are equal to 9 cords of wood for 
fuel, and a family burn 31.5 cords of wood in a year, 
how much will they save by changing from wood to 
coal, when wood is worth $4.25 per cord, and coal $6.80 
per ton? 

208. When it is 12 o’clock mM. at St. Paul, 93° 10’ 
W. Longitude, what is the time at Richmond, 77° 27” 
W.? 

209. Reduce .06875 to the form of a common frac- 
tion and to its lowest terms. 

210. 24 is per cent of what number? 

411. What will $25,390 amount to in 7 mo., at 10 per 
cent? 


18 THE REGENTS’ QUESTIONS. 


212. When gold is worth 124, what amount of cur- 
rency can be bought for $5,400 in gold? 

213. A.’s property is assessed at $6,750, and B.’s at 
$13,575. <A.’s tax is $32.65: how much is B.’s? 

Fiid the unknown term in the following proportions: 

214. V4 3 64:: sib 

215. ti gy 3 i— 





Le. 
216. What is the square root of 1127750724? 


we Eee | yee 


217%. Add in figures, LXAVI, MDXIX, CCIV, XVIII. 

218. From sixty-eight million nine hundred thousand 
and six, take seven million two hundred thousand and 
two. 

219. Six hundred and four is one factor, ninety-six 
thousand and seventy-three is the other: what is the 
product? 

220. Which term in division corresponds with the 
product in multiplication? 

221. Give the method of proving division. 

222. Resolve 7498 into its prime factors. 

223. Find the greatest common divisor of 505, 707, — 
and 4343. 

224. Of what is the least common multiple of several 
numbers the product? 

225. Find the smallest number that exactly contains 
78, 156 and 390. 

“226. Express in words 749293. 

227. Reduce 387 to eighty-fifths. 

228. What is the cost of four fields, containing re- 
spectively 44, 24, 33, and 14% acres, at $25 an acre? 


ARITHMETIC, 19 


229. What is the rate per hour of a boat that goes 
23042 miles in 183 hours? 

230. Write as a decimal, ;32415. 

231. Required the area in acres, etc., of a piece of 
land .5 of a mile long and .3 of a mile broad. 

232. From 1 tb. Troy, take 10 0z. 17 pwt. 18 gr. 

233. Sold 517 bbl. of flour for $8.10 per bbl., at a 
profit of 8 per cent.; what was the whole cost? 

234. Lrd. : 4 ft. :: 2 : $0.50. 

235. (2) 4=? 

236. What is the square root of .0011943936? 

237. What is the amount of $50, at compound inter- 
est for 3 years, at 8 per cent., interest payable half- 
yearly? 

238. A note for $486, dated September 7, 1863, was 
endorsed as follows: Received, March 22, 1864, $125. 
Noy. 29, 1864, $150. May 13, 1865, $120. What was 
the balance due April 19, 1866, the rate being 6 per 
cent? 

239. What are the proceeds of a note for $426.10, 
payable in 5% days, with interest at 6 per cent, dis- 
counted at bank for 6 per cent? 

240. If $400, at 7 per cent., in 9 mo., produce $21 
interest, what will be the interest on $360, for 8 mo., at 
6 per cent? 





(Solve by proportion.) 


Oo Bey wie 


241. Multiply twenty-nine million two thousand nine 
hundred and nine, by four hundred and four thousand. 
242. Divide 478656785178 by 56789. 


r 


20 THE REGENTS QUESTIONS. 


243. Prove that your solution of the last example is 
correct. 

244. A gem weighing 2 oz. 18 pwt. 12 gr. was sold 
for $1.37 per grain: what was the sum paid? 

245. Venus is at a certain time 3 8. 18° 45’ 15” east: 
of the sun; Mars, 7 8S. 15° 36’ 18” east of Venus; Ju- 
piter, 5 S. 21° 38’ 27” east of Mars: how far is Jupiter 
east of the sun? 

246. What is the least common multiple (or dividend) 
of 3, 4, 5, 6, 7 and 8? 

247. What is $ of = of ¢ of 4 expressed in lowest 
terms? 

248. Add t of % to + of =. 

249. Divide 814 by 94. 

250. What is the greatest common divisor of 3, 4, 
and 1}? 

251. Multiply eighty-seven thousandths by fifteen 
millionths. 

252. What decimal fraction is equivalent to 7? 

253. Reduce 6 fur. 8 rd. to the decimal of a mile. 

254. What is the value of .815625 of a pound Troy 
expressed in oz. pwt. and gr.? 

255. If $800 gain $32 in 8 mo., what is the rate per 
cent? 

256. If aman travels 117 miles in 15 days, employing 
only 9 hours a day, how ‘ar would he go in 20 days, 
traveling 12 hours a day? 

257. What is the square root of 9754.60423716? 
~ 258. If the extremes are 11 and 74, and the common 
difference 7, what is the sum of the series? 

259. A man having $10,000, lost 15 per cent of it, 
what sum had he left? 


ARITHMETIC. 21 


260. What is the interest of $850 for 1 year 7 mo. 18 
days, at 7 per cent.? 

261. How long must $165 be on interest at 6 per cent. 
to gain $14.85? 

262. What is the present worth of $477.71, due 4 years 
hence, discounted at 6 per cent? 

263. What is the present worth of a note for $875.35, 
payable in 7 mo. 15 days, discounted at bank at 7 per 
cent? 

264. If 29 tb. of butter will purchase 40 tb. of cheese, 
how many pounds of butter will buy 79 ib. of cheese? 


ace ee 
265. Numerate, read or express in words 8096392702. 


Hott One OOrn 
CO OO oD =H © i 


266. Find the sum of =a See 
i 

267. 2579584239456 —249187654116=? 

268. Multiply four hundred and sixty-two thousand 
six hundred and nine, by itself. 

269. Divide 1521808704 by 6505456. 

270. If the remainder is 17, the quotient 610, and the 
dividend 45767, what is the divisor? 

271. Resolve 7498 into its prime factors. 

272. Find the greatest common divisor of 285 and 465. 

273. What is the least common multiple, or dividend, 
of 16, 40, 96, and 105? 

274. In 4 da. 4 hr. 45 min., how many seconds? 

275.. Reduce 4, 4, 4, 4, 4, 4, 4, 4, to equivalent frac- 
tions having the least common denominator. 

276. Reduce 4 oz. 6 pwt. 93 gr. to the fraction of a 
pound. 


0 
ve 
"9570 
84998 
451786 
467 


22 THE REGENTS’ QUESTIONS. 


277. How many sq. ft. in the four side walls of a 
room 16% ft. long, 15 ft. wide, and 9 ft. high? 

278. The product of three numbers is £; two of the 
numbers are 23 and 4: what is the third? 

279. Add together 423 ten-millionths, 63 thousandths, 
25 hundredths, 4 tenths, and 56 ten-thousandths. 

280. What cost 5 T. 17 cwt. 20 tb. of hay, at $30.50 
per ton? 

281. Reduce 10 oz. 13 pwt. 9 gr. to the decimal of a 
pound Troy. 

282. Divide 0.01654144 by 0.0018. 

283. One acre of corn yields 80 bushels, another acre 
20 per cent more; how many bushels does the second 
acre yield? 

284, What is the amount of $794 for 4 years and 4 
months, at 7 per cent? 

285. What is the bank discount of $600 for 3 mo., at. 
6 per cent? 

286. If 33, of a ship cost £273 28. 6d., what will 
cost? 

287. If $200 gain $12 in one year, what will $400 gain. 
in 9 months? 

288. Find the square root of 434, 


MOTHER OO Se 


289. Write in figures each of the following numbers, 
add them, and express in words (or numerate) their 
sum: fifty-six thousand, and fourteen thousandths; nine- 
teen, and nineteen hundredths; fifty-seven, and forty- 
eight ten-thousandths; twenty-three thousand five, and. 
four tenths, and fourteen millionths. 


ARITHMETIC, 23 


290. What is the difference between 3? plus 7@ and 4 
plus 23? 

291. In multiplying by more than one figure, where 
is the first figure in each partial product written, and 
why is it so written? 

292. If the divisor is 19, the quotient 37, and the re- 
mainder 11, what is the dividend? 

293. What is the quotient of 65 bu. 1 pk. 3 qt. di- 
vided by 12? 

294, Which one of the fundamental operations (or 
ground rules) of arithmetic is employed in reduction 
ascending? 

295. In exchanging gold dust for cotton, by what 
weight would each be atanete 

296. Which is the largest prime number kel 100? 

297. How many weeks in 8568456 minutes? 

298. To what term in division does the value of a 
common fraction correspond? 

299. What is the product of a fraction multiplied by 
its denominator? Give an example. 

300. What is the rule for the multiplication of deci- 
mals? 

301. How is a common fraction reduced to the deci- 
mal form? Give an example. 

302. What is ratio and how may it be expressed?  []- 
lustrate by one or more examples. 

303. If 27 T. 3 qr. 15 lb. of coal cost $217.83, what 

will 119 T. 1 qr. 10 lb. cost? 

304. Find the cost of the several articles, and the 
amount of the following bill: 


24 THE REGENTS’ QUESTIONS. 


ALBANY, October 1, 1870. 
A. P. JEWETT to SAMUEL PaLMkER, Dr. 
To 16750 feet of boards at $12.50 per M., - - 





“SAL FOO" TRE ae 24.00 <§ - - - 
‘on QOOr tins «6 RDO0m, £% or oe) Fe 
Received payment, $ 


SAMUEL PALMER. 
305. What is the length of the side of a cubical box 
which contains 389017 solid inches? 
306. What is the present worth of the following note 
discounted at bank, and when will it become due? 


$100. Utica, October 11, 1870. 
Ninety days from date, for value received, I promise 
to pay to the order of John Smith, one hundred dollars, 
at the Albany City National Bank. 
JOHN Brown. 


307. Involve 3 to the 7th power. 

308. What is the square root of .0043046721? 

309. Sold 94 cwt. of sugar at $84 per cwt., and there- 
by lost 12 per cent: how much was the whole cost? 

310. A person owned 2 of a mine and sold # of his 
interest for $1,710: what was the value of the entire 
mine? 

311. When it is 2 hr. 36 m. A.M. at the Cape of Good 
Hope, in longitude 18° 24’ east, what is the time at 
Cape Horn, in longitude 67° 21’ west? 

312. What is the cost of 17 T. 18 ewt. 1 qr. 17 lb. of 
potash at $53.80 per ton? 


ee Ase 


313. Express in words the number 42567000129301. 
314. Multiply five hundred and forty thousand six 
hundred and nine by seventeen hundred and fifty. 


ARITHMETIC, 25 


315. Give the rule for reduction descending. 

316. How many steps. of two and one-half feet each, 
would a man take in walking a mile? 

317. How is a whole number reduced to a fraction of 
the same value having a given denominator? 

318. What is the value of 2 of 2 of 4 of + when re- 
duced to a simnple fraction of the lowest terms? 

319. Give the rule for reducing several fractions to 
equivalent fractions having the least common denomi- 
nator. 

320. Add 3% to 4214. 

321. Write in figures, two and six hundred-millionths. 

322. Reduce ;4; to the equivalent decimal form. 

323. Multiply seven thousand and five, by three-hun- 
dred-and-five millionths. 

824. Divide .5 of 1.75 by .25 of 174. 

325. The ratio of two numbers is 9, and the antece- 
dent 90; what is the consequent? 

326. Find the value of the omitted term in the fol- 
lowing proportion: 

ES (rp eee es Wa 

327. If 56 lb. of butter cost $15.68, what will .078 of 
a ton cost? 

328. If 96 horses eat 192 tons of hay in one winter, 
how many tons will 150 horses eat in 6 winters? | 

329. In 1 yr. 4 mo., $311.50 amounted to $336.42 at 
simple interest: what was the rate per cent? 

330. What is the interest of $14,231.50 from June 15, 
1865, to April 30, 1870, at 8 per cent? 

331. What 1s the value of a pile of wood 34 ft. long, 
3 ft. wide, and 54 ft. high, at &7.88 per cord? 


26 THE REGENTS’ QUESTIONS. 


332. How much will it cost to carpet a parlor 18 feet 
square, with carpeting ? yd. wide, at $1.50 per yard? 

333. Thegifference in the local time of two places is 
2 hr. 18 m.:"what is the difference in longitude? 
' 334, 33 is 22er cé what number? 

335. What is the lefigtHin rods of each side of a 
square field which contains 66 A. 1 R. 9 sq. rd.? 

336. A note for $470.66 drawn at 60 days, is dis- 
counted at bank at 6 per cent: what are the proceeds? 


a nae 


337. Arrange the following numbers as required for 
addition, and find their sum; 70100.3042875; 20514471; 
641077.21875; 2564308.875; 320538. 609375; 102572353; 
1282154.4375; 90169.0004; 5128617.75; 160269.3046875. 

338. What special name or names are given to the 
period (.), as an arithmetical sign; and what is its use 
in arithmetic? 

339. What two denominations of currency are sep- 
arated and distinguished from each other by the period 
used as an arithmetical sign? 

340. Mention two or more arithmetical processes or 
rules in which ‘‘ Pointing off into periods” is required? 

341. Point off into periods and numerate 70100.- 
3042875. 

342. What arithmetical operation would change the 
value of 320538.609375 to 32.0538609375? 

343. Subtract 70100.3042875 from 102572353. 

344. Multiply 1282154.4375 by 90169.0004. 

345. Divide 102572354 by 641077.21875, and indicate 
by the use of the proper arithmetical sign, whether the 
quotient 1s an integral, fractional or mixed number. 


ARITHMETIC, QC 


346. Change the decimal part of 90169.0004 to the 
form of a common (or vulgar) fraction, and then reduce 
it to its lowest terms. 


347. Find the prime factors of e ee part of 
70100.3042875. 


348. Regarding 20514471 as so many ‘square inches, 
how many square acres, roods, rods, feet and inches 
would be the equivalent of this expression? 

349. Regarding the fractional part of 2564308.875 as. 
the decimal of a pound avoirdupois, to how many ounces. 
would it be equivalent? 

350. Represent the first four figures of 160269.3046875: 
by the Roman notation. 

351. Copy the following bill of items, find the cost of 
each item, insert it in its proper place on the right, and 
find the total amount: 

ALBANY, May 30, 1871. 
Mr. J. B. WoopwortH, 
To A. &#.C. Koonz, Dr. 

To 75 yds. carpeting, @ $2.50............. $ 

ee cruecet, @ $1875.20. 6.700% 5. 
STIS, (OBO ORO os, oo ed eee eield > bea acne hb 

Beet A (D DA2 BO os ce ny xiv ota alan monies er = 

Bett SVOSCOUCIONN, (@ S110. 0. ste ets ing os 


Received Payment, 

i; A. & HE. C. Koonz, 

352. Suppose that you buy of D. Appleton & Co., of 
New York, 5 reams of note paper, at $3.25 per ream;, 
4,500 envelopes, at $4.75 per M.; 24 boxes of steel pens, 
at $1.123 per box; 6 French dictionaries, at $1.50 each; 
and 3 photographic albums, at $5.75 each. Make out 
the bill in regular form, as in question 351. ~/7// ¢ 4 


238 THE REGENTS’ QUESTIONS. 04 


7 nN 
‘ 7 t/ 
v 


353. Suppose that the Messrs. Appleton consent to 
discount 12 per cent from the amount of the foregoing 
items, how much would the required payment become? 

354. Analyze (or explain in words the method of 
solving) the following example: If 6 men can do a 
piece of phase in 10 days, how long will it take 5 men to 
lo it? A. 

305. Define Ratio. : 

356. Define Proportion. 

357. Define Rule of Three. 

358. Solve the following example by the Rule of — 
"Three (or Proportion): 

If a railroad car goes 17 miles in 45 minutes, how far 
will it go in 5 hours at the same rate? 0° ~ - 


359. J. Ayres had D. Howe’s note for $1, 228, dated 


Dec. 29, 1869; what will be the amount Oct. 9, 1872, at 
‘9 per cent. ? 271a¥ 

360. What apace will gain $5.11, in 3 yr. and 6 
mo., at 8 per cent.2. /& / ‘ 


eae pf (a 


361. Express by figures the number: Sn trillion 

eighty billion nine millions and one. 6 ©? ¢ 07 ff“ 
- 362. Add the following numbers: 

(1) Two hundred and ten thousand four hundred; 

(?) One hundred thousand five hundred and ten; 

(3) Ninety thousand six hundred and eleven; 

(+) Forty-two hundred and twenty- ives, : 

(°) Hight hundred and ten. e.£ 9 


363. Taking two hundred and ten chopseet four hun- 
dred as a minuend, and one hundred thousand five 


ARITHMETIC, 29 


hundred and ten as a remainder, what will the subtra- 
hend be, expressed in words? // ¥ } 7 @ 

364. What is the product of ninety tivasand six hun- 
dred and eleven, and forty-two hundred and twenty- 
five? S&F <9 “SA? 

365. The quotient of one number divided by another’ 
is 37; the divisor, wee the remainder, 230: what is the: 
dividend? - YS se 

366. What is the rout common divisor of 1649 and 
5423? “id 

367. What is the least common multiple (or ee 
of 21, 35, and 42? 2/ 0 

368. What is the value of 62 divided by 8%? = 4 s 
_ 369. How many yards of cloth 4 of a pv wide are: 
equivalent to 12 yards ? yards wide? / 

370. Change 4 to an equivalent fraction having 91 for 
its denominator. — 4 

371. The difference between $ and § of a number is: 
10: what is that number? J GD 

372. What 1 is the sum of 4, 1445, 10%, and 5? / ‘ 2é ty 

373. What will 4868 bricks cost, at "$4. "5 per M.? / & 

374. An open court contains 40 square yards: how 
many stones, nine inches square, will be required to 
pave it? 644 © 

375. Change .0008 to a common MADRS Ne 

376. Change <3, to a decimal. 

77. How many cords of wood ale be piled in a shed. 
50 ft. long, 25 ft. wide and 10 ft. high? | 

378. How many acres of city land at $2 per square’ 
foot, could be bought for a half million dollars? 

379. Change 10 oz. 13 pwt. 9 gr. to the decimal of a 
pound Troy. 


J “j F, 
7, 


30 THE REGENTS’ QUESTIONS. 


380. A man owning 4 of an iron foundry, sold 35 per 
cent of his share: what part did he still own? 

381. What will be the amount, at simple interest, of 
$35.61, from Noy. 11, 1869, to Dec. 15, 1871, at 6 per 
cent? 

382. If the consequent be 7, and the ratio ?, what is 
the antecedent? 

383. At the rate of 9 yards for £5 12s. how many 
yards of cloth can be bought for £44 16s.? 

384. What is the square root of 576.02880036? 


ee 


385. Add seven hundred and four; sixty thousand 
four hundred; five million eight thousand and sixty; 
912875; thirty thousand and forty-nine; seven hundred 
and seven thousand nine hundred and six. 

. 886. A. had $3,958, B. $1,463; A. lost $1,365, B. 
gained $1,165: which then had the most, and how 
much? 

387. A peddler bought 491 yards of cloth at 81 cts. a 
yard; he used 29 yards, and sold the rest at 95 cts. a 
yard: how much did he gain? 

388. A city had $311,205 at the beginning of the 
year; the income of the year was $884,743, and the ex- 
penses $896,756: what was the balance on hand at the 
end of the year? 
~ 889. A man exchanged 159 cords of wood at $5 a 
cord, for a horse valued at $144, and the balance in 
sheep at $3 apiece: how many sheep did he receive? 

390. How many pieces of muslin, each containing 33 
‘yards, must be sold at 14ct. 5 m. a yard to realize 
$1,339.80? 


ARITHMETIC. 31 


391. Ilow many sq. yd. of paving in a street are 
there, 2700 ft. long and 40 ft. wide? 

392. At noon on Thursday, a ship was in north lati- 
tude 28° 15’ 35”; it then sailed north till Saturday 
afternoon at 3 0 piicaees when it was in north latitude 41° 
34’ 35": what was the average motion per hour, in geo- 
graphical miles? 

393. § of » of 14 of 3 of & of 204 = ? 

394. Sold a team for $1834, losing $243: for how 
much should I have sold it to gain $397, 

395. A man having 1053 A. of land exchanged ¢ of it 
for wood, at the rate of 10} C. per A.: how many C, 
did he receive? 

396. Multiply the quotient of 14%, divided by 6% by 
the quotient of 53 divided by 74> 

397. Reduce 9000000 in. to mi. 

398. What is the cost of a field 77 rd. long and 41 rd. 
wide, at $17.60 an A.? 

899. If 4.2 yd. of cloth costs $15, what will 8 yd. 3 
qr. cost? 

400. If a loaf weighing 124 oz. is worth 2 igen .» When 
flour is $4 a bbl., what. is me value of a loaf weigh- 
ing 10% oz. when flour is $62 a bbl. ? 

401. A man bought 350 A. of land for $40 an acre, 
and sold a part for $2,240, at the same rate: what per 
cent. of the land did he sell? 

402. At 6 per cent, what is the interest of $720 for 3 
yrs. 4 mo. 16 da.? 
~ 403. Sold 50 bbl. of wine, each containing 31 gal. 2 
qt., at $2.40 a gal., receiving a note at 90 days without 
grace: what would be the proceeds of this note, dis- 
counted at 75 per cent? 





32 THE REGENTS’ QUESTIONS: 


404, A., B. and C. bought a horse for $100 and sold 
him for $150, by which A. gained $18 and B. $19: how 
much had each paid for the horse? | 

405. A man had a yard 38 ft. long and 27 ft. wide: 
he reserved two grass plats each 8 ft. square, and had 
the rest paved with stone, at 45 cts. a sq. yd.: what did 
the paving cost? 

406. The product of two equal factors is 34225: what _ 
is each factor? 

407. Find the sum of 10 terms of the geometric series, 
3, 6, 12, ete. 

408. If January 1st is Sunday, how much can a man 
earn in the first three months of a leap year, at $1.25 
per day, not working Sundays? 


sb deal gp eyh vith ac 


409. If the minuend be 69 trillion and the difference 
85 billion, what is the subtrahend? 

410. If 892 is one factor, and 28544 the product, 
what is the other factor? 

411. Resolve 180 into its prime factors. 

412. Find the greatest common divisor of 222 and 
564. 

413. Reduce 8692 to a fraction whose denominator is 
25. 

414, What cost 54 cords of wood at $7.56 a cord? 

415. $ of 19 divided by +, of $ of $ = ? 

416, A body of 4800 troops has 4 as many cavalry as 
infantry: what is the ee of infantry? 

417, 394284748 =? 

418. The product of three numbers is 744; two of 
them are 84 and 6,: what is the third? 


' ARITHMETIC, 33 


419. Reduce 2 mi. 5 f. 13 r. 4 yd. 2 ft. to inches. 

420. What would be the cost of enough oil cloth to 
cover a room 12x164 ft. at 75 cents per sq. yd.? 

421. At $198 per lb., what would be the cost of 10 
oz. 10 pwt. 10 gr.-of gold? 

422. What is the difference in time of two places 
whose longitudes differ 7 degrees, 8 minutes and 4 
- seconds? 

423. Write in figures (the fractional part as decimal) 
the number: seven million and one ten-millionths. 

424, 49.2654756 divided by .0750 = ? 

425. Reduce .8975 of a week, to whole numbers of a 
lower denomination. 

426. What is the amount of $1,000 for 7 yr. 10 mo. 
18 da., at 6 per cent. simple interest? 

427. What is the present worth of $1,609.30 for 10 
mo. 24 da., discounted at 5 per cent? 

428, For what must apples, which cost $1.25, be sold 
to gain 20 per cent? 

429, If $800 yield $56 interest in a certain time, what 
will $390 yield at the same rate? 

430, If a 3-cent loaf weigh 2 oz. when flour is $7.50 
per bbl., what should a 12 cent loaf weigh when flour is 
$16 per bbl. ? 

431. What number expresses the difference between 
the square and the cube of 24? 

432. What is the square root of 253009? 


Rn Eg Yeh 


433. Write in figures: twenty quintillion two hun- 
dred and seven billion six hundred million six thousand 


and fifty-nine. 


34 THE REGENTS’ QUESTIONS. 


434. Express in words: 224000000600317010. 

435. Add 100375, 406780,4673005, 4112, 18365791, 
2478, etal 164357. 

436, Find the sum (in Roman notation) of LXVI, 
MDXIX, CCIV, XVIII. 

437. The factors of a certain number are 53, 7, 5, and 
107: what is that number? . 

438, 246515999541 divided by 28653=? 

439. What are the prime factors of 6006? 

440. What is the greatest common divisor of 2268 and 
344? 

441. Find the least common multiple of the 9 digits. 

442. Reduce 3, +45, $, and 24, to equivalent numbers - 
having the least common denominator. . 

443, What would be the whole cost of four fields, 
containing respectively, 44, 23, 3%, and 14% acres, at 
$25 an acre? / 

444, Reduce 3x$x5x4xX15 x! x, toa single frac- 
tion of the ee terms. 

445, If a man makes $147 on the sale of one table, 
how many tables must he sell to make $273? 

446. A. Barnes, of Lee, sold B. Brown the following 
articles: April 1, 1872, 24 yd. black silk, at $2.25 a 
yd.; April 3, 2 pieces of calico, 40 yds. each, at 30 cts. 
a yd.; May 2, 4 dress patterns, at $6.75 a pattern; May 
9, 225 yd. linen, at $1.12 a yd. Brown paid $55 on ac- 
count. Make out his bill in proper form, showing 
balance due. 

447, At 35ce. per sq. yd., what would it cost to plaster , 
a wall 15 ft. high and 54 ft. long? 

448. How much wood in three piles, the first of 


ARITHMETIC. 35 


which contains 10 ed. 6 ed. .ft. 4 cu. ft., the second, 12 
ed. 12 cu. ft.; the third, 17 cd.:1 cd. ft.? 

449, Divide the sum of five thousand and two thou- 
sandths, by two hundredths. 

450. $10 is 12 per cent of what number? 

451. What is the amount of $2,160 from March 10 to 
Dec. 1, at 5 per cent? 

452. How much must be invested at 7 per cent sim- 
ple interest to yield an annual income of $630? 

453. A note for $1,800, payable in 60 days, was dis- 
counted at bank at 6 per cent: how much did the 
holder receive? 

454, What cost 9 hats, if 5 hats cost £4, 5s. ? 

455. If the wages of 6 men for 14 days are $126, what, at 
the same rate, would be the wages of 9 men for 16 days? 

456. Extract the square root of 6.5536. 


seed Sy 


457. Write in words the number represented by the 
figures: 20463162486135. 
458. Express in figures: fifty-seven billion fifty-nine 


million ninety Pinned and forty-seven. aX 


HBSS BSS ERSSSESA fe 
459. Add ae SHRSAS BPH 


5432 


460. From 501505010678 take 794090589. 

461. Multiply ninety thousand eight hundred and 
seven by nine thousand one hundred and six. 

462. 18 A. 0 R. 14 p. equal how many square feet? 

463. 31557600 seconds equal how many days? 

464. From 61 8. 15° 36’ 15” take 53 8S. 18° 50’ 18”. 

465. If 84 loads of hay weigh 201 T. 6 cwt. 0 qr. 12 
1b., what will 5 loads weigh? 


36 THE REGENTS’ QUESTIONS. 


466. What are the prime factors of 19965? 

467. Find the least common multiple of 3, 4, 5, 6, 7, 
8. 

468. Reduce 3x3; xX + x82? x4/ to a simple fraction 
of the lowest terms. 

469. Reduce 4, %, 4, $+, } and 5 to equivalent frac- 
tions having the least common denominator. 

470. What is the sum of #, $, 2, and jy? 

471. Divide 1163 by 144. (Give the answer as a 
mixed number, with its fraction of the lowest terms. ) 

472. Reduce 4 of a grain to the fraction of a pound 
Troy. | 

473. Paid $4,355.52 for 498 pieces of carpeting: what. 
would 374% pieces cost, at the same rate? 

474. Multiply eighty-seven thousandths by fifteen 
millionths. 

475. What decimal fraction is equivalent to 74? 

476. What is 5 per cent of $789? 

477. What is the interest of $1,165.50, for 5 yr. 3 mo. 
9 d. at 7 per cent? 

478. What is the bank discount on $780 for 30 days? 

479. If A. travels 117 miles in 15 days employing 9 
hours a day, how far would he travel in 20 days, travel- 
ling 12 hours a day (at the same rate per hour)? 

480, What is the square root of 23804641? 


Ma listas, | | ak. 
481. Write 1873 in Roman characters. 
482. What is Notation ? 
483. Write in words 9008007006. 


484, To what number must 962 be added three times 
to make 8472? 


ARITHMETIC. Ot 


485. $9,843.621 plus $4,687.32 plus $84.321 plus $.07 
plus $.64 plus $973.241 = ? 

486. Reduce 53684” to numbers of higher denomina- 
tions. 

“487. Reduce .8975 of a week to whole numbers of 
lower denominations. 

488. What cost 102 tons of coal at $75 a ton? 

489. 108-12 x 7 -—$=? 

490. Find the least common multiple of 12, 16, and 28. 

491. Reduce 42, 42, and 8% to the least common de- 
nominator. 

-492. A cubic foot of granite weighs 163 Ib. 5 oz.: 
what is the weight of a block 3 ft. 22 in. long, 2 ft. 
4 in. wide, and 1 ft. 3 in. thick? 

493. How many linear yards of carpeting 14 yd. wide 
will cover a floor 18 ft. square? 

494. When snow is uniformly 6 inches deep, how 
many cubic feet are there on one acre of land? 

495. Charles Fuller bought of James Monroe, at West 
Troy, N. Y., May 4, 1873, 1 horse for $95, 2 cows at 
$50 each, 1 wagon for $62, 2 shovels at $1.12 each and 
30 bushels of corn at $0.65 per bushel, paying cash in 
full. Make the bill in due form. 

496. A cistern can be emptied by 7 pipes of equal 
capacity in 35 minutes: in what time can it be emptied 
if only 5 pipes are open? 

497, If 12 per cent of $97.50 be lost what amount will 
_ remain? 

_ 498. What is the simple interest of $200 for 4 yr. 6 
mo. 3.d., at 7 per cent? 

499. Find the bank discount of $1,000 for 3 mo. at 7% 
per cent. 


38 THE REGENTS’ QUESTIONS. 


500. If 9 lb. of lead make 150 bullets, how many bul- 
lets can be made from 105 lb.? 

(Solve by proportion and cancellation. ) 

501. If the wages of 75 boys for 84 days were $68.75, 
how many days could 90 boys be employed at the same 
rate, for $41.25? 

(Solve by double proportion. ) 

502. What is the difference between the square and 

the cube of 24? 


503. What is the square root of 253009? 
504. $ of a number exceeds 4 of it by 20: what is that 
number? 








22 


505. Find the sum # of 93 and 4 of 281. 

506. Find the difference between 32-+ 72 and 4+ 23. 

507. The product of three factors is 193, and two of 
them are ¢ and 3: what is the other? 

508. Divide .5 of 1.75 by .25 of 173. 

509. What is the value of 62 divided by 8%, as a sim-: 
ple fraction? 

510. What is the value of .815625 of pound Troy ex- 
presssed in oz. pwt. and gr.? 

511. Reduce 4da. 4 hr. 48 mi. to the decimal of a. 
week. 

512. A person owned 2 of a mine and sold $ of his 
interest for $1,710: find the value of the entire mine. 

513. Sold 92 cwt. of sugar at $8 per cwt., and thereby 
lost 20 per cent: what was the whole cost? 

514. A man owning 4 of a bank, sold 35 per cent of 
his share: what per cent of the whole was left? 


ARITHMETIC, 39 


515. A.’s property is assessed at $6,750, and B.’s at 
$13,550. A.’s tax is $55.35: how much is B.’s? 

516. How many acres can 10 men plough in 14 hours 
if 7 men plough 6 acres in 123 hours? 

517. What is the simple interest on $200 for 3 yr. 10 
mo. at 7 per cent? 

518. In 1 yr. 4 mo., $311.50 amounted to $348.88, at 
simple interest: what was the rate per cent? 

519. What is the amount of $1,000 for 7 yr. 10 mo. 
18 da., at 6 per cent simple interest? 

520. What sum, at 9 per cent, simple interest will 
amount to $286.00, in 3 yr. 4 mo.? 

521. A note for $470.66 drawn at 60 days, is dis- 
counted at bank at 6 per cent: what are the proceeds? 

522. What is the amount of $50, at compound inter- 

est for 3 yr. at 8 per cent, interest payable half-yearly? 
— §23. J. Ayres has D. Howe’s note for $1,728, dated 
Dec. 29, 1869: what was the amount Oct. 9, 1873, at 9 
per cent, with interest from date? 

524. What is the value in currency of $865 in gold, 
when the latter is selling at 107 per cent? 

525. How much gold will $100 currency buy, gold 
being at 111? 

526. Suppose that you buy of D. Appleton & Co., of 
New York, 5 reams of note paper, at $3.25 per ream; 
4,500 envelopes, at $4.75 per M.; 24 boxes of steel pens, 
at $1.124 per box; 6 French dictionaries, at $1.50 each; 
and 3 photographic albums, at $5.75 each. Make a bill 
for D. Appleton & Co., against yourself, in regular 
form. 

527. A man had a yard 38 ft. long and 27 ft. wide; 
he reserved two grass plats, each 8 ft. square, and had 


a 


40 THE REGENTS’ QUESTIONS. 


the rest paved with stone, at 45 cts. a sq. yd.: what did 
the paving cost? 

528. How much will it cost to dig a cellar 40 ft. long, 
82 {t. wide, and 5 ft. deep, at $0.25 a cubic yard? 


Soe A pe 


529. Find the smallest number which will exactly 
contain 9, 15, 18, 20. 

530. If 5 be added to each term of the fraction 4, by 
what number will its value be diminished? = 4 

531. If .0001 is the dividend, and 1.25 the divisor, 
what is the quotient? 

532. What will 28 Sq. yd. 129 pe. ft. of land cost at 
aft cts. per sq. ft.2 £4 

. What is the cost of 4,565 feet of joist, at $23 

bie NE and 13,640 ft. of boards at $53.55 per M.?) 2 yoy 

534. If 323 sq. yd. of carpeting will cover a floor 14 
ft. wide, what is the length of the floor? / 

535. Ifa load of wood is 8 ft. long and 3 ft. wide, 
how high must it be to contain a cord? %~ * 

536. “What decimal of a short ton is 2 of an 02.2. 77/?/ 

537. 20004-+(20.104% 5.07) —(6.44-+.0005) =? 19 250942 

538. What part of 22 is (2 of 2 of 3+2)? dh, 

539. Reduce .3945 of a day to lower denominations.” 

540, An agent received $67.50 for collecting $4, 500: 
what was the rate per cent of his COTTA STGHER i 

541. How many cubic ft. in a rectangular beam, 24 
ft. 6 in. long, 1 ft. 9 in. wide, and 1 ft. 23 in. thick? 

542. How much shall I gain by borrowing $3560 for 
1 yr. 6 mo. 10 da., at 6 per cent, and lending it at 7 per 
cent for the same length of time? 


ARITHMETIC, 41 


543. What is the amount of $1,450.40 from April 19, 
1872, to August 3, 1873, at 6 per cent? 

544, What is the difference between the greatest com- 
mon divisor of 30 and 42, and their least common mul- 
tiple? 

545. A 63 gal. cask is 3 full of wine; if 27.625 gal. 
should leak out, the wine remaining will be what deci- 
mal part of the full cask? 

546. James Riley & Co. bought, July 7, 1873, of 
Joseph Herr, Trenton, N. J., 15 tons of coal at $6.50 
per ton; 19 tons of coal at $8.25 per ton; and 143 cords 
of wood at $5.20 per cord. Make a bill of the purchase, 
and receipt it for Joseph Herr. 

547. How much must be paid for 41 gal. 2 qt. 1 Rt 
of molasses, at 72 cts. a gal.? 

548. If 14 of a ton of hay cost $18.50, how muck will 
two loads eas one weighing 2 of a ton, and the other 
43 of a ton? 

549. What is the difference between the true and the 
bank discount of $300, for 3 months, at 8 per cent? 

550. What principal on interest at 7 per cent from 
‘—~ April 9, 1871, to Sept. 5, 1873, will amount to $1,477.59? 
*?P- 551. The difference between the interest of $600 and 
that of $750, at 5 per cent for a certain time is $18.75. 
What is the time? 

552. If 18 men can dig a trench 30 yd. long in 24 da. 
by working 8 hr. a day, how many men can dig a trench 
60 yd. long, in 64 da., working 6 hours a day? 


sain Y wl 


553. What is the sum of 3912, 400005, 6312, 736863, 
-C00803, 60708010, 44,5. 290.68042? 


42 THE REGENTS QUESTIONS. 


~ 


5. What will 250 miles of telegraph wire cost at 3 
cts. per ft.? 

556. When it is noon at the Cape of Good Hope, in 
longitude 18° 24’ east, what is the time at Cape Horn, 
in longitude 67° 21’ west? 

557%. How many cords of wood in a pile 140 ft. long, 
44 ft. wide, and 64 ft. high? 

558. Required the area in acres, etc., of a piece of land 
.5 of a mile long, and .3 ot a mile broad. 

559. How much will it cost to dig a cellar 40 ft. long, 
32 ft. wide, and 5 ft. deep, at $0.25 a cubic yard? 

560. 4 of a qr. is what per cent of 2 of a cwt.? 

561. Reduce 4 tb. Troy to units of lower denomina- 
tions. 

562. How much gold will $100 currency buy, gold 
being at 113? 

563. In 1 yr. 4 mo., $311.50 amounted to $336.42, at 
simple interest: what was the rate per cent? 

564. What sum, at 7 per cent, simple interest, will 
amount to $221.07, in 3 yr. 4 mo.? 

565. A note for $470.66, drawn at 60 days, is dis- 
counted at bank at 6 per cent: what are the proceeds? 

566. What is the amount of $50, for 2 yr., at 8 per 
cent, compound interest, payable half-yearly? 

567. The four sides of my garden are 168 ft., 280 ft., 
182 ft., and 252 ft., respectively. What is the greatest 
length of boards that I can use in fencing it, without 
cutting any of them? 

568. A garden has 4 sides, respectively 168, 280, 182, 
and 252 ft. long. Suppose that each board is 8 in. 


554. Subtract s4, of 93, from 5% of 1514. 
oo 


- ARITHMETIC. 43; 


wide, and that the fence is 5 boards high: how many sq. 
ft. of boards will it require to fence the garden? 

569. Suppose that you sell to John Clarke of New 
York for cash, 75 yd. of carpet, $1.55 per yd.; 30 yd. 
drugget, at $1.30 per yd.; 5 mats at $3.15 each; and 35 
yd. of oil cloth, at $1.05 per yd. Make a receipted bill. 
of these articles, in regular form. 

570. What is the value of (2 x $+ 32) + 23? 

571. What is the least number that 8, 12, and 16 will 
each divide without remainder? 

572. What. will 11 ib. 4 oz. of tea cost, if 3 tb. 12 02. 
cost $3.50? 

(Solve by proportion. ) 

573. If a man travels 107 miles in 15 days, employing 
only 9 hours a day, how far would he go in 20 days, 
travelling 12 hours a day, at the same rate per hour? 

574. What debt can be discharged in a year by weekly 
payments in arithmetical vrogression, the first being: 
$24, and the last $1,224? 

575. What is the length in feet and inches, of each 
side of a square carpet, made from 2084 yds. of Brussels. 
carpeting, ¢ yd. wide? 

576. What is the length of the side of a cubical box 
which contains 389017 solid inches? 


25 








577. Find the sum of the following numbers, arrang-- 
ing them properly for addition: 14.2351; 651.012; 
2.319; .0374; .00146. 

578. Multiply 4.44; 5.555; 6.23; .5. 

579. Divide 6.435945 by 4027.5. 

580. Find the sum of 164, $4, and 81. 


44 THE REGENTS’ QUESTIONS. 


581, Find the product of $$, §, and 3. 

582. If 32 bu. of oats cost $23, what will 2 bu. cost? 

583. Resolve 122,850 into its ie factors. 

584. Find the greatest common divisor of 195, 285, 
and 315. 

585. Find the least common multiple of 49, 14, 84, 
168, and 98. 


586. Sold 2,462 feet of boards, at $ 7.25 per 1000 
ee 600°" “scanthngy? >‘! tea ee 
et tL sO.L2 teases rile kes [Sod Doro OG 
re 77 ** hewn timber “< 1b CK etoet 


Write a bill of the same and receipt it. Tre seller 
may be John Smith, and the buyer James Brown. 

587. What part of } of a mile is 4% rods, expressed in 
decimals? 

588. The longitude of New York city is 73° 58’ 54.43” 
W.; of Buffalo, 78° 53’ 25” W. What is the difference 
of time? 

589. Write the rule for multiplication of decimals. 

590. Write the rule for division of decimals. 

591. Define ratio, state how it may be expressed, 
what each term is called, and give an example. 

592. The same of proportion. 

593. What is either extreme of a proportion equal to? 
What either mean ? 

594. What is the simple interest on $2,500 for 1 yr. 8 
mo. 12 da., at 7 per cent? 

595. A. has a note against B. for $1,728, payable 90 
days after date, without interest, which he gets dis- 
counted at bank at the rate of 7 per cent: what does he 
receive? 

596. Extract the sq. root of 1104601. 


ARITHMETIC, AB 


597. If a man can do a piece of work in 20 days, 
working 10 hours a day, how long will it take him to do. 
the same if he works 12 hours a day? 

(Solve by proportion. ) 

598. A farmer Due a flock of sheep in three as eS; 
in the first he puts 4 of his flock, in the second 4, and 
in the third, 32 sheep. How many has he? 

(Solve by analysis. ) 

599. Find 12 per cent of $75. 

600. A commission merchant sold 500 pieces of mus- 
lin, each piece containing 21 yards, for 23 cents a yard: 
what is his commission at 23 per cent? 


See a NY 9 ee 


601. The population of Me. is 627,413; of N. H., 
301,471; of Vt., 300,187; of Mass., 1,240,499; of Conn., 
410,749; of R. L., 192,815. What is the aggregate pop- 
ulation of these States? 

602. B. had $12,311; and after paying his debts, and 
giving away $2,108, he has $8,199 left. What was the: 
amount of his debts? 

603. How many peaches in an orchard of 14 rows of 
trees, each row having 27 trees, and each tree 108 
peaches? 

604. How many cheeses of 45 fb. each, at 12 cts. 
per ftb., will pay for 15 bbl. of apples, each containing 3 
bu., at 84 cts. per bu. ? 

605. Add 8-8, 2%, and 3%. 

606. What cost 334 fb. of tea, at 93? cts. per fb? 

607. 1003%+-663=? 

608. Write as a decimal, and in words, 5,485. 


46 THE REGENTS’ QUESTIONS. 


609. 6.43875+4027.5=? 

610. Anna Lee buys of Eva Cole, for cash, 18 yd. of 
calico, at 124 cts. per yd.; 12 yd. muslin, at 17 cts.; 24 
yd. linen, at 74 cts.; and 9 spools of thread, at 7 cts. 
Make a bill in due form. | 

611. What decimal part of a mile is 74 rd. 5 yd.? 

612. The circumference of one carriage wheel is 13 ft. 
9 in., and that of another is 16 ft. 6in. How many 
more times will one turn than the other, in going 30 
miles? 

613. What cost 8,824 th. of hay, at $15 per ton? 

614. The means and one extreme of a proportion be- 
ing given, how may the other extreme be found? 

615. The extremes and one mean being given, how 
may the other mean be found ? 

616. Give an example of a proportion in which the 
means and one extreme are given, and solve it. 

617. Give an example of a proportion in which the 
extremes and one mean are given, and solve it. 

618. If 20 yd. of cloth # of a yd. wide are required 
for a dress, what must be the width of a piece 12 yd. 
long, to answer the same purpose? 

(Solve by proportion. ) 

619. If aman can walk 250 mi. in 9 da. of 12 hr. each, 
how many da. of 10 hr. each would he spend in walking 
400 mi.? (Solve by double proportion. ) 

620. A boy bought eggs at the rate of 3 for 5 cts., 
and sold them at the rate of 4 for 7 cts., clearing 9 cts.: 
how many did he buy? (Solve by analysis. ) - 

621. A commission merchant sold 500 pieces of cloth 
for $30 a piece, and paid the owner $14,700: what was 
the rate of his commission? 


ARITHMETIC, 47 


622. A store was insured for $12,000 at the rate of 2 
per cent, and the goods for $15,000, at 1¢ per cent: 
what was the entire premium? 

623. What will be the proceeds of a note for $1,000, 
without interest, payable at bank in 60 days, at 6 per 
cent? 

624. A man being asked his age, replied, if you add 
to its half, its third and three times three, the sum will 
be 130: what was his age? 


4.1105) us 


625. The quotient is 71, the divisor 42, and the re- 
mainder 15: what is the dividend? 

626. What will be the cost of 3,760 tb. of hay at 
$8.50 per ton? 

627. From 174 take 3 of 164, and multiply the re- 
mainder by 3. 

628. A lady bought 6 silver spoons, each weighing 
3.0z. 8 pwt. 8 gr., at $2.25 an oz., and a gold chain 
weighing 14 pwt., at $1.25 a pwt.: what was the cost of 
both spoons and chain? 

629. From 15 ten-thousandths take 27 millionths, 
and multiply the difference by 20.5. 

630. Reduce 6.25 of a pound Troy to lower integers. 

631. How many seconds are there in the three sum- 
mer months? 

632. How many acres are there ina street 4 rods wide, 
and 24 miles long? 

633. Reduce 4s. 6d. to the decimal of a £ sterling. 

634. A quantity of sugar was bought for $150, and 
sold for $167.50: what was the gain per cent? 

635. Mrs. C. B. Jones bought of Cole, Steel & Co., 


48 THE REGENTS’ QUESTIONS. 


of Detroit, as follows: Nov. 12, 1874, 23 yd. calico, @ 
l6c.; 45 yd. sheeting, @ 20c.; Dec. 7, 12 yd. silk @ 
$1.623; 8 handkerchiefs, @ 45c.; 2 pairs kid gloves, @ 
$1.873. Make bill for Jan. 1, 1875, and receipt the 
same, as clerk of the firm. 

636. What is the interest of $125.50 for 7 mo. 10 da. 
at 7 per cent? 

637. A note for $500, dated Oct. 8, 1873, and bearing 
interest at 9 per cent, is endorsed as follows: Nov. 4, 
1874, $36; Jan. 30, 1875, $250. What will be due July 
1, 1875? 

638. What is the true discount on $236, due in 3 
years, at 6 per cent? 

639. What is the bank discount on $125 payable in 90 
days, at 8 per cent? 

640. ‘wo men divided a lot of wood costing $81, one 
taking 53 cords, and the other the remaining 8 cords: 
what must each pay? (Solve by analysis.) 

641. What is the square root of 416.16? 

642. How many gallons of water will a cistern hold 
which is 7 ft. long, 6 ft wide, and 11 ft. deep? 

643. A. can mow 2 acres in 3 days, and B. 5 acres in 
6 days: in how many days can they together mow 9 
acres? 

644, A house valued at $3,240 is insured for 4 of its 
value, at # per cent: what is the premium? 

645, How many bricks will it require to build a wall 
2 rd. long, 6 ft. high, and 18 in. thick, each brick being 
8 in. long, 4 in. wide, and 23 in. thick? 

646. If the wages of 24 men for 4 days are $192, what 
will be the wages of 36 men for 3 days? 

(Solve by double proportion and cancellation. ) 


ARITHMETIC, 49 


647. At what rate per cent will $311.50 amount to 
$337.40 in 1 year, 4 mo.? 

648. What will it cost to lay a pavement 36 ft. long, 
and 9 ft. 6 in. wide, at 40 cts. a sq. yd.? 


28 


649. Express in words the number: 42567000129301. 

650. Multiply five hundred and forty thousand six 
hundred and nine, by seventeen hundred and fifty. 

651. Give the rule for reduction ascending (0. ¢. from 
lower to higher denominations), and state how this pro- 
cess chiefly differs from reduction descending. 

652. How many steps of two and one-half feet each, 
would a man take in walking five miles? 

653. How is a whole number reduced to a fraction of 
the same value, having a given demominator? 

654. What is the value of 2 of 2 of 4 of 4, when re- 
duced to a simple fraction of the lowest terms? 

655. Give the rule for reducing several fractions to 
equivalent fractions having the least common denomi- 
nator. 

656. Add 33%, 4%4, and: 51.652. (Express the frac- 
tional part of the sum as a decimal of three places. ) 

657. Write in figures: two and six hundred-millionths. 

658. Reduce <4; to the equivalent decimal form. 

659. Multiply seven thousand and five, by three- 
hundred-and-five-millionths. 

660. Divide .5 of 1.75 by .25 of 174. 

661. If 27 T. 3 qr. 15 tb. of coal cost $217.83, what 
will 119 T. 1 qr. 10 tb. cost? (First reduce qrs. and 
fbs. to the decimal of a ton; and then solve by propor- 
tion.) 








50 THE REGENTS’ QUESTIONS. 


662. What is the square root of .0043046721? 

663. The ratio of two numbers and the consequent 
being given, what is the process for finding the anteced- 
ent (considering it as standing in the same relation to 
the consequent, as a numerator to its denominator) ? 

664. Find the value of the omitted term in the fol- 
lowing proportion : $4: (?)::9 : 16. 

665. A note for $486, dated Sept. 7%, 1873, was en- 
dorsed as follows: Received, March 22, 1874, $125; May 
13, 1875, $120. What balance remained due at time of 
last payment, the rate being 6 per cent? 

666. What is the length of the side of a cubical box 
which contains 103823 solid inches? 

667. What are the proceeds of the following note dis- 
counted at bank, and when will it become due ? 
$100. Utica, October 11, 1875. 

Ninety days from date, for value received, I promise 
to pay to the order of John Smith, One Hundred Dol- 
lars, at the Albany City Bank. JOHN JAY. 

668. Involve 2 to the 5th power. 

669. Sold 94 cwt. sugar at $84 per cwt., and thereby 
lost 12 per cent: what was the first cost? 

670. A person owned 2 of a mine, and sold # of his 
interest for $1710: what was the value of the entire 
mine? 

671. When it is 2h. 36’ A.M. at the Cape of Good 
Hope, in longitude 18° 24’ east, what is the time at 
Cape Horn, in longitude 67° 21’ west? 

672. What is the cost of 17 T. 18 cwt. 1 qr. 17 tb of 
potash, at $53.80 per ton? (Iirst reduce the lower de- 
nominations to the decimal of a ton.) 


ARITHMETIC. OL 


eb cedars O19 es ale Mie 


673. Two men are 450 miles apart; if they approach 
each other, one traveling 30 miles a day and the other 
35 miles a day, how far apart will they be at the end of 
6 days? 

. 674. A. had $24, B. four times as much as A. less $16, 
and C. twice as much as A. and B. together plus $17: 
how much money had C.? 

675. Give all the prime numbers below 20; and all 
the composite numbers between 20 and 40 inclusive. 

676. What is the greatest common divisor of 144, 
216, and 648? 

677. Reduce to the simplest form (20%+4 of 2) +63 
—3x$. 

78. The longitude of New York being 3° E. from 
the meridian of Washington, San Francisco 45° 25’ W., 
what will be the the time of day at New York, when it 
is noon at San Francisco? 

679. 2 pk..3 qt. 1.2 pt. is what decimal part of 20 bu. ? 

680. What will it cost to dig a cellar 40 ft. long, 21 
ft. 6 in. wide, and 4 ft. deep, at $1.75 a cubic yard? 

681. From 16 ten thousandths take 27 millionths and 
multiply the difference by 20.5. 

682. Henry Smith bought of John Clarke, of Louis- 
ville, Ky., as follows: Dec. 10, 1875, 7 pair calf boots 
@ $5.75; 6 pair ladies’ gaiters @ $3.25; 10 pair chil-, 
dren’s shoes @ $1.75; Jan. 5, 1876, 12 pair coarse boots 
@ $3.124. Make out and receipt the bill, as clerk of 
John Clarke. 

683. A clerk receiving a salary of $950, pays $275 a 


52 THE REGENTS QUESTIONS. 


year for board, $180 for clothing, and $150 for other 
expenses: what per cent of the salary is left? 

684, Carriages costing $165 are sold at 18 per cent. 
profit; what is the gain on each carriage? 

685. A school house is insured at 2 per cent and the 
premium was $93.60: for how much is the house in- 
sured? 

686. If a man’s pulse beat 300 times in 4 minutes, 
how many times will it beat in 8 hours? (Solve by 
proportion. ) 

687. If it cost $84 to carpet a room 36 ft. long and 21 
ft. wide, what will it cost to carpet a room 33 ft. long 
and 27 ft. wide? (State and solve as a wae pro- 
portion. ) 

688. At what date will a note for $300, given Jan. 10, 

1876, amount to $347.25, at 6 per cent simple interest? 

689. A note for $520, dated April 12, 1874, had the 
following endorsement: ‘‘ Dec. 6, 1874, $120.” What 
amount will be due May. 1, 1876, at 9 per cent, simple: 
interest? 

690. What is the square root of 10403? 

691. A flag pole 180 ft. high casts a shadow 135 ft. in 
length: what is the distance from the top of the pole to 
the end of its shadow? 

692. A block of granite in the form of a cube con- 
tains 41063.625 cubic inches; what is the length of its 
edge? 

ao Of) eee 


693. The Erie Railway is 460 miles long, and cost. 
$65,000 a mile: if $9,645,635 had been paid, how much 
would remain unpaid? 


ARITHMETIC, DS 


694. How many bb. of butter, at 33 cts. a tb., can be 
bought for 55 tb. of tea, at 78 cts. a tb.? 

695. What is the sum of twenty-nine and three tenths, 
four hundred and sixty-five, and two hundred and 
twenty-one thousandths? (Give the answer in figures 
and also in words.) 

696. If I own § of a farm, and sell 3 of my share for 
$2,300, what is the value of the whole farm at the same 
rate? 

697. Find the factors of .035, and multiply .007853 
by these factors. 

698. Reduce 15 cwt. 3 qr. 24 tb. to the decimal of a 
ton. 

699. Reduce 4%, to a decimal (of 9 places). 

700. The four walls of a room are each 16 ft. in length 
and 9 ft. in height, and the ceiling is 16 ft. square: how 
much will it cost to plaster it, at 14 cts. a sq. yd? 

701. A merchant failing in trade, pays 65 cts. on each 
dollar owed; he owes A. $2,750, and B. $1,975; how much 
does he pay each? 

702. Paid $41.624 for a pile of wood, at the rate 
of $3.37% a cord: how much was there in the pile? 

703. A steamship, in crossing the Atiantic, has 3,500 
miles to go: if she sails 211 mi. 4 fur. 32 rd. a day, what 
distance, after 15 da., has she still to sail? 

704. How many sq. ft. are there in a board 17 ft. 6 
in. in length, and 1 ft. 7 in. in width? 

705. A pasture of a certain extent supplies 30 horses 
for 28 days: how long will the pasture supply 21 horses? 
(Solve by proportion. ) 

706. If 4 bbl. of flour cost $343, how much can be 
bought for $182? (Solve by analysis.) 


54 THE REGENTS’ QUESTIONS. 


707. How much hay will 32 horses eat in 120 days, if 
96 horses eat 32 T. in 7$ weeks? (Solve by compound 
proportion. ) 7 

708. What is the simple interest of $2,594.20 for 10 
mo. 9 da., at 7} per cent? 

709. What is the compound interest of $1,250, for 2 
yr. 3 mo. 24 da., compounded annually, at 6 per cent? 

710. What is the bank discount on a note for $556.27, 
payable in 60 days, discounted at 6 per cent? 

711. Two merchants enter into partnership. One 
puts in $5,000 and the other $2,000. ‘The partner that 
puts in the less sum is to receive $300 extra from the 
proceeds for his superior knowledge of the business. 
They gain $4,725: what is the share of each? 

712. What is the 3d power of 8.628? 

31 —— 

713. How many figures are in each of the periods into 
which numbers are divided for reading? 

714. Name the first four periods of integers, and the 
first three orders (or places) of decimals. 

715. Write in figures the number: One million one 
thousand one hundred and one. 

716. Write in figures the numbers: Forty- seven, three 
hundred and fifty thousandths, forty-two millionths, 
two hundred and twenty-three billionths. 

717. Multiply 732.53 by 37.846. 

718. Divide 6052.74 by 4.379. 

719. Bought a box of soap containing 70 tbs. Keeping 
it all summer, it dried away 4, when I sold it at 8% cts. 
per pound. I gave 7 cts. per pound. Did I make or 
lose? How much? 





ARITHMETIC, D5 


720. If 20 men require 73 bbl. of flour for their sub- 
sistence five months, how much will 30 men require for 
a year? 

721. What is the value of 7, of 74 of a vessel, ifa 
person who owns 33; of it sells $ of § of his share for 
$1,750? 

722. Write the following numbers in the decimal 
form, and then add them: 64, 124, 52, 63, 2, 2. 

725. Multiply 5 da. 15 hr. 13 m. 208. by 341. 

724, Allowing a person to perform a certain journey 
in 133 days, by travelling 10 hours a day, in what time 
ought he to perform the journey if he travel 114 hours 
per day? 

725. What.is the cost of a load of hay weighing 1,875 
lb., at $12.50 per ton (2000 lbs.) ? 

726. What ought eggs to be per pound, when they are 
selling at 18? cts. per dozen, if they average 93 eggs to 
a pound? 

727. How many cords in three piles of four ft. wood, 
the first 36 ft. long and 4 ft. high, the second 42 ft. 
long and 5 ft. high, and the third 20 ft. long and 6 ft. 
high? 

728. What would it cost to enclose a square lot con- 
taining 160 acres, with a fence costing at the rate of $4 
per rod? 

729. A note of $65.80, dated Feb. 20, 1868, and bear- 
ing interest at 7 per cent, was paid June 25, 1870: what 
was the amount paid? 

730. What is the amount of $152 at semi-annual com- 
pound interest for 2 years, at 6 per cent per annum? 

731. What is the annual premium on a policy which 


56 THE REGENTS’ QUESTIONS. 


insures a house worth $12,000 for 4 its value, at + per 
cent? 

732. Amount $102.81, on $74.50, at 10 per cent. 
What is the time? 


apne Ser ee 


733. Name the first six periods in numeration. 

734. Express in figures: one trillion six thousand. 

%35. 1 million 400 thousand and 50+15 hundred+25 
thousand+-120 thousand 6 hundred and 14=? 

736. The subtrahend is 2603.46, and the remainder is 
72.804; what is the minuend? 

73%. The factors of a number are 7300.96 and 5.006; 
what is the number? 

738. The dividend is 39314.76, and the quotient is 
%.071: what is the divisor? 

739. What operations may be performed on the terms 
of a fraction without altering its value? 

740. If the numerator be equal to the denominator, 
what is the value of the fraction? 

741. How does multiplying the numerator affect the 
value of the fraction? : 

742. How does multiplying the denominator affect 
the value of the fraction? 

743. Change 124 to an improper fraction. 

744. Reduce #? of 4 of {45 of 14 to a simple fraction. 

745. Multiply 48; of 124 by 4 of 73. 

746. Divide $ of 14 by 2 of 4. 

747. In what terms of multiplication may equal fac- 
tors be cancelled? 

748. In what terms in division may equal factors be 
cancelled? 


ARITHMETIC, at 


749-750. A note for $250, dated June 5, 1874, was 
paid Feb. 14, 1875, with simple interest at 8 per cent. 
What was the amount? (Two credits. ) 

751. What is Ratio? 

752. How is Ratio expressed ? 

753. What is Proportion. 

754. How is Proportion expressed ? 

755. What are the lst and 3d terms of a Proportion 
called ? 

756. What are the 2d and 4th terms of a Proportion 
called? 

757. What are the extremes of a Proportion, and 
what the means? 

758. Given the means and one extreme of a Propor- 
tion, how may the other extreme be found? 

759. Given the first, second and fourth terms of a 
Proportion, how may the third be found? 

760. In the question: If 4 tons of coal cost $24, what 
will 12 tons cost, what is the given ratio? 

761. If 4 tons of coal cost $24, what will 12 tons cost? 
(Solve by proportion.) 

762. Change +=4? to the form of a proportion. 

763-764. ia is 73° 44” 50” West Longitude: 
San Francisco is 122° 26’ 45". When it is noon at 
Albany, what is the time at San Francisco? (Two 
credits. ) 

765. What will $864.50 amount to in two years at 8 
per cent. compound interest? 

766. If 10 tons of hay will support 5 horses 8 mo., 
how many horses will 18 tons support one year? (Solve 
by double proportion. ) 

767. How many men will be required to build 32 rods 


58 THE REGENTS’ QUESTIONS. 


of wall in the same time that 5 men will build 10 rods 
(Solve by analysis. ) 


—— 33 —— 


768. What are the 3 terms in multiplication called? 

769. What are the 3 terms in division called? 

770. What are the first and second terms in multipli- 
cation taken together called? 

771-772. To what terms in multiplication do the 
terms in division correspond? 

773. How many partial products will there be, if the 
multiplier consists of several figures? 

774, Given 73654 a multiplicand, and 4365 a multi- 
pler, give each successive multiplier, expressed in words; 
(775) express each partial product im words; (776) ar- 
range these products properly in figures for addition, 
and find the entire product. 

777. To what, in division, does the numerator of a 
fraction correspond? 

778. To what, in division, does the denominator of a 
fraction correspond? 

779. If a cubic foot of lmestone weigh 175 hb., 
what is the weight of a cubic yard? 

780. What part of an acre is ¢ of a square rod? 

781. Find the greatest common divisor of 72, 96, 120, 
384. 

782. Divide 6525 by 4.35. 

783. Add 4, #, +4, 7%. 

784, Find the product of -§, «124x474. 

785. Divide 2 of 24 by ¢ of 3. 

786. Reduce to an equivalent decimal 54,. 


ARITHMETIC. 59 


787. If 104 cords of wood cost $34.124, what will 602 
cords cost? (Solve by analysis. ) 

788. How much carpeting ? of a yard wide, is re- 
quired for a room 27 ft. 3 in. long and 22 ft. 6 in. 
wide? 

789. In multiplication of decimals, how is the place 
of the decimal point in the product determined? 

790. In division, how is the place of the decimal ° 
point in the quotient determined? 

791. At $1.20 per gallon, what cost 1 bbl. 15 gal. 3 qt. 
of molasses? 

792. Reduce 28 rd. 4 yd. 2 ft. 10 in. to inches. 

793. What per cent of $4 are 30 cents? 

794. Sold 160 acres of land for $4,563.20, which was 
8 per cent less than it cost: what did it cost per acre? 

795. What is the simple interest of $137.25 for 2 yr. 
7 mo. 14 da. at 7 per cent? 

796. A note for $250, dated June 5, 1874, was paid 
Feb. 14, 1875, with interest at 8 per cent. What was the 
amount ? | 

797. Bought two horses for $420, paying $48 more 
for one than the other. Find the price of each. . 

798-799. Boston is 71° 4’ 2” W. longitude, and Wash- 
ington 77° 1’ 30”. When it is noon at Boston, what is 
the time at Washington? (Two credits.) 

800. If 2375 A. 2 R. 16 rd. of land be laid out in 
the form of a square, what will be the length of each 
side? 

801. A. has $4,000, B. $2,700, C. $2,300 in a house 
renting for $720: what is each man’s share of rent? 

802. What is the present worth of $2,000 due in 3 
yr. 6 mo., with interest at 7 per cent? 


GO THE REGENTS QUESTIONS. 


Oo 


803. In the decimal notation, why is the nought (0) 
used, which of itself has no value? 

804. Why does (0) annexed to the decimal not change 
its value? 

805. What is the difference between a common and 
‘a decimal fraction? 

806. A man gave 503 acres of land to his sons, giving 
them 834 acres each: how many sons had he? 4 ~“«z 

807. What is the value of a fraction multiplied by its 
denominator? 

808. If 14 acres of meadow yield 32% tons of hay, 
what will 53 acres produce at the same rate? _ 

809. Change 4, 2.17, .136, and .0408 to equivalent 
decimals having a common denominator. (810.) Find 
their sum. fe 

811-12. A farmer sold 300 bu. of oats at $0.45 a bu, 
and 162 cords of wood at $3$ a cord. He received in 
payment 125 Ib. of sugar at $0.123 a tb., 36 fb. of tea’ 
at $f a tb., 6 bbl. of flour at $8.373 a bbl., and the rest 
in cash. How much cash did he receive? 

813. Divide 100 by .001. 

814. What is the cost of 536720 bricks, at $8.75 per M. ? 

815. How many coats can be made from 32. 4 pas of 
cloth, allowing 2.7 yds. for each coat? _ 

816. Find the prime factors of 2205. 

817. Divide 375287 by 46; (818) write the several 
parts into which the dividend is separated in the process 
of division, each exactly containing the divisor; (819) 
. show that the sum of these parts with the remainder 





ARITHMETIC. 61L. 


(if any) equals the dividend; and (820) that the sum of 
the several quotients expresses the whole quotient. 

821. Find the greatest common divisor in 72, 126, 216. 

822. What is Percentage? 

823. How may the percentage of a number be found? 

824. Mention three arithmetical operations in which 
percentage is used. 

825. What is the interest on $4,010 for 1 yr. 1 mo. 13 
da. at 7 per cent simple interest? 

“826. What is the commission on the sale of a house 
for $9,346.80, at 64 per cent? 

827. If $4.30 is paid for an insurance of $860, what. 
is the rate? 

828. In a proportion, the two extremes and one mean. 
being given, how may the other mean be found? 

829. In what terms of a proportion may equal factors 
be cancelled? 

830. If a man walk 192 mi. in 6 da., walking 8 h. a 
day, how far can he walk in 18 days, walking 6 hours a 
day? (Solve by compound proportion.) 

—831. If 251 A. 65 P. of land are laid out in form of 
a square, what will be the length of each side? 

832. How many sheets of tin each 14x22 in., will 
it take to cover a roof, 30 ft.x18 ft. 4 in.? 

833-837. At $0.36 per sq. yd., for plastering, and 
$0.75 per roll for paper hanging, how much will it cost 
to plaster the walls and ceiling, and paper the walls of a 
room 18x16x9 ft., making allowance, in papering, for 2 
windows, each 3x6 ft., and 3 doors, each 3x7 ft., the 
paper being 1 ft. 6 in. wide and 7 yd. in a roll? (2 cred- 
its for computing plastering surface correctly; 2 for 
papering; and 1 for cost.) 


62 THE REGENTS’ QUESTIONS. 


USSG ere 


838. How many pounds of tea, at 72 cents a pound, 
would pay for 3 hogsheads of sugar, each weighing 
1464 pounds, at 15 cents a pound? | 

839. A teamster agrees to cart 132 bbl. of flour for a 
merchant on Monday, 84 on Wednesday, and 108 on 
Friday; what is the largest number he -can carry at a 
load, and yet have the same number in each? 

840. In 3 how many ninety-eighths? 

841. How many yards in three remnants of cloth con- 
taining respectively 24 yd., 14 yd., and 2¢ yd.? 

842. The sum of two numbers is 59$, and the greater 
is 3032: what is the other number? 

843. Find the value of (23-+34) x (84—43). 

844. How many cords in a pile of wood 196 ft. long, 
7 ft. 6 in. high, and 8 ft. wide? 

845-46. What will be the cost of removing the earth 
from the cellar of a house 48 ft. 9 in. long, 32 feet wide, 
and 9 feet deep, at $0.57 per cubic yd? (2 credits: 1 for 
contents in cu. ft.; 1 for cu. yds. and price.) 

847. A. has 25 per cent of his property invested in a 
house, 10 per cent in a farm, 5 per cent in a barn, and. 
the rest ina grove worth $4,800. What is the amount 
of his property? | 

848. Bought a barrel of syrup for $20; what must I 
charge a gallon in order to gain 20 per cent on the 
whole? 

849. B. sends $6,897.12 to his agent in New Orleans, 
requesting him to invest in cotton after deducting his 
commission at 2 per cent: what was the sum invested? 


ARITHMETIC, 63 


- 850. It costs me $72 annually to keep my house in- 
sured for $18,000; what is the rate? 

851. The difference in the time of St. Petersburgh 
and Washington is 7 hr. 9 min. 193 sec. What is the 
difference in the longitude of the two places? 

852. What is Insurance? 

853. What is the Policy? 

854. What is the Premium? 

855. A man bought a farm, giving a note for $3,400¢ 
payable in gold in five years; at the expiration of the 
time gold was 175 per cent: what did his farm cost in 
currency? 

856. Find the simple interest of $460.90 for 3 yr. 
5 mo. 13 da. at 33 per cent. 

857. C. bought a house for $3,486, which rents for 
$418.32. What rate per cent does he make on the in- 
vestment? 

858. Find the compound interest of $380.80 for one 
year at 8 per cent interest payable quarterly. 

859. What is True Discount? 

860. What is Bank Discount? 

861. What is the difference between the dank and 
the ¢rue discount on $1,000 at 7 per cent, payable in 90 
days? 

862. What are the terms of Ratio severally called? 

863. How is the ratio of two given numbers found? 

864. Reduce the ratio 65 : 85 to its simplest terms. 

865. Of how many ratios, at least, must a proportion 
consist ? 

866. The average cost of keeping 25 soldiers one 
year is $3,000; what would it cost to keep 139 soldiers. 
7 years? (Solve by proportion.) 


64 ' THE REGENTS’ QUESTIONS. 


867. Find the square root of 466,489. 

868-69. A pile of cord wood is 256 ft. long, 8 ft. high, 
and 16 ft. wide; what would be the length of each side 
of a cubical pile containing the same quantity? 


36 


870. The Atlantic cable cost as follows: 2500 miles @ 
#485 per mi.; 10 miles deep sea cable @ $1,450 per mi.; 
25 miles shore ends @ $1,250 per mi. What was the 
cost? 

871. What is the number which divided by 453 gives 
the quotient 307, and the remainder 109? 

872. Which are the so called ‘‘ Fundamental Rules” 
of arithmetic? and (873), why are they so called? 

874. What is a prime factor ? 

875. Find the prime factors of 2366. 

76. A man working for $2 a day, and paying $4 a 
week for board, saved $72 in ten weeks. How many 
week-days was he idle? 

877. What is a fractional unit ? 

878. Reduce 54, »;, 34 and 44 to the least common 
denominator. 

879. From 284 subtract 33. 

880. Divide #,x4% by $x EX X34 X51, 

881. Divide 46.1975 by 54.35. 

882. From a hogshead of molasses, 28 gal. 2 qt. were 
drawn: what common fraction represents the part of a 
hhd. which remained? 

883. What decimal part of a fathom is 32 ft.? 

884. If the consequent be 34 and the ratio 7, what is 
the antecedent? 

885. When are ¢hree numbers said to be proportional? 








ARITHMETIC. 63 


886. If a water pipe discharge 24 bbl. in 1 hr. 14 m., 
in what time will it discharge’ 54 bbl.? (Solve by 
analysis. ) 

887. What is the cube root of 19.54, carried to 4 dec- 
imal places? 

888. If it cost $95.60 to carpet a room 24x18 ft., how 
much will the same kind of a carpet cost for a room 
38 22 {t.? (Solve by proportion. ) 

889. What sum of money is that of which, if 80 per 
cent be deposited in bank, and 20 per cent of this de- 
posit be drawn, there will remain $5,760 in bank? 

890. A lawyer collecting a note at a commission of 8 
per cent thereon, received $6.80. What was the face 
of the note? 

891. Bought stock at par, and sold it at 3 per cent 
premium, thereby gaining $750: how many shares, of 
$100 each, did I buy? 

892. What is the amount of $16,941.20, for 1 yr. 7 
mo. 28 da. at 4% per cent simple interest? 

893, An investment of $7,226.28 yields $744.7937 an- 
nually: what is the rate of interest? 

894, In what time will $273.51 amount to $312.864, 
at 7 per cent simple interest? 

695. What is the difference between the interest and 
the discount of $576, due 1 yr. 4 mo. hence, at 6 per 
cent? 

896. Three men gain $2,640, of which B. is to have 
$6 as often as C. $4 and A. $2: what was each one’s 
share? | 

897. Find the square root of 10795.21. 

898. What is the length of one side of a square piece 
of land containing 40 acres? 


66 THE REGENTS’ QUESTIONS. 


899. How is the true discount of a note found? 

900. How is the bank discount of a note found? 

901. How is the present worth of a note payable at a 
future time without interest found? 


pide 3 ip lle 


902. Write in figures: two hundred thousand two 
hundred. 

903. A man owns farms valued at $56,800; city lots 
valued at $86,760; a house worth $12,500; and other 
property, $6,785: what is the entire value of his prop- 
erty as. 

904. Bought 325 loads of wheat, each load containing 
50 bu., at $2 a bu. What did the wheat cost? 

905. Find the greatest common divisor of 679 and 
1,869. 

906. Find the least common multiple of 4, 16, 20, 48, 
60, and 72. 

907. What is the valwe of a fraction? 

908. Find the value of ;435. 

909. If the divisor is less than a unit, how will the 
quotient compare with the dividend? 

910. Divide 63 by 4%. 

911. Find the difference between the continued pro- 
ducts of 3, $, $, 4%, and 34, 2, 4, 2. 

912. If 36.48 yd. of cloth cost $54.72, what will 14.25 
yd. cost? 

913. A goldsmith manufactured 1 tb. 1 pwt. 16 gr. of 
gold into rings, each weighing 4 pwt. 20. gr. He sold 
them for $1.25 apiece: how much did he receive for 
them? 


ARITHMETIC, 67 


914. How many times will a wheel 16 ft. 6 in. in cir- 
cumference turn round in running 42 miles? 

915. What is the value of 3 of a hogshead, in integers 
of lower denominations? 

916. Washington is 77° 2’ 48” west, and St. Peters- 
burg 30° 19’ east longitude: what is their difference of 
time? 

917. What is 94 per cent of 275 miles? 

918. A man sends $3,246.20 to his agent in Boston, 
asking him to lay it out in shoes, after deducting his 
commission of 2 percent. How much is his commission? 

919. A gentleman has a house insured for $8,000, and 
the furniture for $4,000, at 2 per cent: what premium 
must he pay? 

920. State the difference between percentage and 
interest. 

921. What is the interest of $1,500.60 for 2 yr. 4 mo: 
at 64 per cent? 

922. Find the amount of $387.20, from Jan. 1 to 
Oct. 20, 1878, at 7 per cent. 

923. A man was offered $3,675 in cash for his house, 
or $4,235 in three years without interest: he accepted 
the latter offer: did he gain or lose, and how much, 
money being worth 7 per cent? 

924. What are the proceeds of a note for $368, at 90 
days, discounted at bank at 6 per cent? 

925. If 16 horses consume 128 bushels of oats in 50 
days, how many bushels will 5 horses consume in 90 
days? (Solve by Compound Proportion. ) 

926. Will the cube of 13 be greater, or less, than that 
fraction, and why? 

927. What is the square root of .00008836? 


68 THE REGENTS’ QUESTIONS. 


928. The pedestal of a certain monument is a cube, 
containing 373,248 solid inches: what is the length of 
one of its sides? 

929. A. loaned $1,600 at 6 per cent, until it amounted 
to $2,000: what was the time? 


930-31. Write and define any four (or more) of the 
following terms: Notation; Roman Notation; Arabic 
Notation; Decimal Scale or System; Duodecimals; Nu- 
merator; Quotient. (1 credit for 2, and 2 for 4 or more 
correct answers. ) 

932. Write 1879 according to the Roman Notation. 

933. Add the numbers: 1, 12, 123, 1234, 12345, 123456,. 
1234567, 12345678, 123456789. 
~ 934. Bought wheat at 94 cts. per bushel, to the 
amount of $59.22, and sold for $70.56: what was the 
selling price per bushel? 

935. When are two numbers prime to each other? 
Give two such numbers, each greater than fifty. 

936-37. Express the following numbers and processes, 
by the proper arithmetical signs, and find the result: 
The fraction whose numerator is 19 and denominator 
760, being increased by ;';, and this sum multiplied by 
the square of 2, becomes a fraction whose square is +. 
(One credit for the expression and one for the solution.) 

938-40. Reduce ($374—$134) x (2 of 8)+23#. (One 
credit for each of the operations indicated by the signs 
2 lian +=) 

941. If 5 be added to both terms of the fraction 3, 
will its value be increased or decreased, and how much? 


ARITHMETIC. 69 





942. Express the value of 7739457, without writing 
the denominator. 

943. On a railroad 57 mi. 133 rd. 114 ft. long, there 
are 9 stations, including those at the two ends of the 
road. What is the average distance between the stations? 

944. If 6 men can build 73 ft. of wall 4 ft. high in 
5 days, how many feet can they build in 33 days? 

(Solve by proportion. ) 

945. A merchant sold 86.55 tons of coal at $5.24 per 
ton; how much did he receive (%, cts., mills)? 

946. In selling 86.55 tons of coal at $5.24 per ton, a 
merchant made $100.63; how much did the coal cost 
him, per ton? 

947. A merchant sold 86.55 tons of coal at $5.24 a 
ton, gaining $100.63; what was his percentage of profit? 

948. Find the difference of longitude between Con- 
stantinople, 28° 59’ E., and Boston, 71° 3’ 30” W. 

949. When it is 12 M. at Constantinople, 28° 59’ E., 
what time A. M. or P. M. isit at Boston, 71° 3’ 30” W? 

950. On what month and day will the following be 
due? 

ALBANY, Fes. 13, 1879. 


Sixty days after date, for value received, I Drona to 
pay John Adams, or order, three hundred and seven ;f5;, 
dollars, at the Albany City National Bank. 


$307 555- THOMAS JEFFERSON. 

51. What would be the rate per cent of interest or 
discount on a note given and payable in this State, no 
rate being expressed ? 

952. What would be the proceeds of a note at 60 days 
for $307,55,, discounted at bank on the same day that it 
was made? 


70 THE REGENTS’ QUESTIONS. 


953. Find the present worth of $890, due in 1 yr, & 
mo., without interest, allowing 8 per cent discount? 

954. How would 7X7X7X7X7X7X7X7X7 be writ- 
ten, according to the notation used in Involution? 

955. Perform the operations indicated as follows: 

/'558009-+ V/=3i,=? 

956. A certain room is 27 ft. long, 18 ft. wide, and. 
10 ft. high. How many pieces of paper 4 yd. wide 
(9 yds. in a piece) will the side walls require, no allow- 
ance being made for doors, windows, etc. ? 

957. How many yards of carpeting, ? yd. wide, would. 
be needed for a room 18 x 27 ft. ? 


Bad ie, ¥ lll e 


958. In multiplication, which factor must be an ab- 
stract number, or used as such? 

959. How many times is 73, contained in 6,000? 

960. The subtrahend being 1487, the minuend 152, 
find the remainder. 

961. How many square feet in a piece of land, 13 
rods square? | 
962. If I buy stocks at 10 per cent below par and sell 
at 10 per cent premium, what per cent do I gain on my 

first Investment? 

963. Find the interest on $5,500 for 1 yr. 6 mo. 9 da. 
at 6 per cent. 

964. When it is noon on the prime meridian, where 
will it be 93 o’clock A. M.? 

965. What will 7,580 bricks cost, at $3.50 per M? 

966. What is the difference between common and 
decimal fractions? 

967. Divide fifteen thousandths by five ten-millionths. 


ARITHMETIC, 71 


968. Find the greatest common divisor of 153 and 187. 

969. Find the least common multiple (or dividend) 
of the same numbers. 

970. A cellar is to be dug 30 ft. long and 20 ft. wide: 
at what average depth will 50 cubic yards of earth have 
been removed? 

971. A. B. and C. trade together. A. puts in $1,000 
for 10 months, B. $800 for 12 months, C. $900 for 14 
months. They gain $1,200. What is the share of 
each? 

972. What is the square root of a number? 

973. Find the sum of the composite numbers below 47. 

974. Name the 4th decimal order. 

$75. Change .03125 to a common fraction, in its 
lowest terms. 

976. If 35 cords of wood cost $11.374, what will 124 
cords cost? (Solve by proportion. ) 

977. John Brown bought of James Ray, on May 20, 
1879, 23 yards broadcloth, at $3.50a yard, 2 pairs gloves 
at $1.874 a pair, 19 yards silk, at $1.75 a yard, and 33 
yards sheeting, at 9 cents a yard. Make a bill m proper 
form and receipt it, as clerk. 

978. How many rods of fence will be required to 
inclose a square field containing 90 acres? 

979. What will be the cost of 4 tb. 5 0z. 6 pwt. of gold 
dust, at 75 cts. per pwt.? 

980. Give the rule for extraction of square root, 

$81. Give the table of linear (or long) measure. 

982. A coal dealer bought 300 long tons of coal at 
$3.75 a ton, and sold it at $4.60 per short ton. What 
was the total profit? 

983. What is the rate per cent of profit in selling 300 


92 THE REGENTS’ QUESTIONS. 


od 


long tons of coal, bought at $3.75 a ton, at $4.60 a 
short ton? 

984. What would be the proceeds of the following 
note discounted at bank on the day that it was made: 

BuFFALO, May 20, 1879. 

Thirty days after date, for value received, I promise 
to pay to the order of John Young, one hundred and 
five ;°,°, dollars, at the Marine Bank. 

$1055. IcHABOD CRANE. 

985. On what month and day must a note for 30 
days, dated May 20, 1879, be paid, or in default of 
payment, be protested? 


REE yf ate E 


986. What number divided by 453 gives 307 as a 
quotient, and 109 as a remainder? 

987. How does a divisor of a number differ from a 
multiple of that number? 

988. Find the greatest common divisor of 56, 140, 
182, and 98. 

989. What are the prime factors of 11970? 

990. Explain the principle (not process) of cancella- 
tion, and illustrate by an example. 

991. What change do we make in the value of a 
fraction if we take the same number of parts but di- 
minish their size? 

992. 3969—13, Why? 

993. Prove that .625 =3 

994. A vat 13 ft. square contains 1224 cu. ft. How 
deep is it? 

995. Change .0000625 mi. to decimal of a foot. 

996. (248 of 7) X (% of 3X4) = what? 


ARITHMETIC. 13 


997. The volume of a cube contains 91125 cu. ft. 
What is the length of each edge of the cube? 

998. How many sq. ft. in the entire surface of a 
cube, each edge of which is 75 ft. ? . 

999. I have an acre of land in shape of a rectangle, 
one side of which is 9 rods in length. What is the 
length of the other side? 

1000. 45%54*8 _ what? 

284-74 

1001. The time at a certain place is 16 hr. 10 m. ear- 
lier than at Greenwich. Give the longitude of the place. 

1002. I have a rectangular field which measures 25 
rods by 10 rods. At $0.40 per yard, what will be the 
cost of boundary fences for the entire field? 

1003. What will be the total cost, at the same rate as 
in Q. 1002, of cross fences to divide the same field into 
lots 5 rods square? Make a small diagram of the field 
and its subdivisions. 

1004. In a school of 300 pupils, the boys are to the 
girls in the ratio of 13 to 17: required the number of 
each? 

1005. If I sell goods at one-half their cost, what per 
cent do I lose, and if at double their cost, what per cent 
do I gain? 

1006. If 18 men can dig a trench 30 yd. long in 5 da. 
of 8 h. each, in how many days of 10h. each can 10 
men do the same work? 

1007. Show that 541, tb. Troy = 44 pwt. 

1008. From % of a day take § of an hour leaving re- 
sult in hours, minutes and seconds. 

1009. What will be the amount in three years of 
$625, compounded at 7% annually? 


V4 THE REGENTS’ QUESTIONS. 


1010. In what time will $240 amount to $720, at 124 
simple interest? 

1011. Find the proceeds of a note for $1255.38 paya- 
ble in 4 mo. 12 da., discounted at bank, interest being 
at 6%. 

1012. What i is the present worth of a note for $1315- 
.39, due in 2 years and 6 months, at 74? 

1013. Sold a horse for $91, which was 4 of what he 
cost me. How much did I lose? 

enemy Gale a 

1014. The quotient of one number divided by another 
is 37, the divisor 245, and the remainder 230: what is 
the dividend? 

1015. Two men start from different places, distant 
189 miles, and travel toward each other; one goes 4 
miles, and the other 5 miles an hour: in how many 
hours will they meet? 

1016. A merchant sold 18 barrels of pork, each weigh- 
ing 200 pounds, at 12 cts. 5 mills a pound: what did he 
receive? 

1017. Suppose a certain township is 6 miles long and 
44 miles wide, how many lots of land of 90 acres each 
does it contain? 

1018. What are the prime factors of 1800? 

1019. Find the greatest common divisor of 1426, 322, 
and 598. 

1020. What is the least common multiple of 9, 17, 6, 
and 27? 

. 1021. Add 214, er ane eo oe 


1022. Reduce =5 to its simplest form. 
: XE 4 


ARITHMETIC, vias 


1023. How many times is .12 of 12 contained in .24 
of 72? 

1024. How many pounds of coffee, at 334 cents per 
pound, can be bought for $14.50? 

1025. What is the cost of 2684 bricks at $8.50 per M. ? 

1026. Required the number of pounds in a hogshead. 
of sugar, weighing 18 cwt. 3 qr. 14 bb. 

1027. Reduce 5, of a ton to integers of lower denom- 
inations. , 

1028. Sold a quantity of merchandise that cost $1670,. 
at a loss of 3%: for what amount did I sell it? 

1029. A house was sold, at an advance of 5% on the 
cost, for $13,000: what was the cost? 

1030. What is the interest of $475, for three years, at 
5% simple interest? 

1031. Required the amount of $1350, from January 
12, 1880, to September 19, 1881, at 9% simple interest. 

1032. What sum of money at 5% simple interest, will 
yield $275.40 in 3 years and 4 months? 

1033. In what time will $3750 amount to $4541.25 at 
6% per annum? 

1034. What is the present worth of a debt of $1650, 
due 8 months hence, without interest, money being 
worth 6%? 

1035. What is the difference between true and bank 
discount on $1000, for 63 days, at 6%? 

1036. Sold flour at $10.45 per barrel, and thereby lost. 
5% of the cost: what was the cost per barrel? 

1037. Suppose a railroad train to run at the rate of 20: 
miles in 50 minutes, in what time will it run 275 miles? 

1038. What will be the wages of 9 men for 11 days, 
if the wages of 6 men for 14 days be $84? 


76 THE REGENTS’ QUESTIONS. 


1039. Find the square root of 149.4, correct to three 
decimal places. 

1040. What is cube root? 

1041. Required the cube root of 1860867. 


42 


1042. What are the fundamental rules of Arithmetic? 

1043. Why are they so called? 

1044. If a scholar’s expenses are 90 dollars for board, 
30 dollars for clothes, 12 dollars for tuition, 5 dollars 
for books, and 7 dollars for incidentals, what would be 
the expenses of 27 boys at the same rate? 

1045. If 256 be multiplied by 25, the product dimin- 
ished by 625, and the remainder divided by 35, what 
will be the quotient? 

1046. What are the terms of a fraction? 

1047. Subtract 120%, from 4504. 











$ of 82 . 
1048. 142, less ig? 38 % of + of what number? 
. 10 


1049. Reduce .9375 to a common fraction. 

1050. How are times will .5 of $1. % be contained. 
in .25 of 174? 

1051. How much must be paid for lathing and plas- 
tering overhead a room 36 feet long and 20 feet wide, 
at 26 cents a square yard? 

1052. Reduce 150 sheets of paper to the decimal of 
a ream. 

1053. A farmer having 760 sheep, cept 25 per cent 
of them, and sold the Pearadon How many did he 
sell? 

1054. What is Commission? 

1055. What is Brokerage? 


vee 


ARITHMETIC, rive 


1056. An auctioneer sold a house for $3284, and the 
furniture for $2176.50; what did his fees amount to, at. 
24 per cent? 

1057. A man purchased $6275 stock in Pennsylvania. 
Coal Company, and sold the same at a discount of 12 
per cent: what was his loss? 

1058. If 123 hundred weight of sugar cost $140, how 
must it be sold to gain 25%? 

1059. What will it cost to insure a factory valued 
at $21,000, at 4 per cent; and the machinery valued at. 
$15,400, at 2 per cent? 

1060. What is the interest on $76.50 for 2 years, 2 
months, at 5 per cent? 

1061. Required the amount of $387.20, from Jan. 1 
to Oct. 20, 1879, at 6%? 

1062. What will $450 amount to in 1 year, at 64% 
compound interest, payable quarterly? 

1063. What is the present worth of $180, Aggie in. 
3 years, 4 months, discounting at 6 per cent? 

1064. Wishing to borrow $500 at bank, for what sum 
must my note be drawn, at 30 days, to obtain the re- 
quired amount, discount being at 6%? 

1065. At what per cent must $1,000 be loaned for 3 
years, 3 months, 20 days, to gain $183.18? 

1066. How long must $204 be on interest at 6% to 
amount to $217.09? 

1067. If a staff 3 ft. 8 in. ice cast a shadow 1 ft. 6 
in., what is the height of a steeple that casts a shadow 
75 tt. at the same time? (Solve by proportion. ) 

1068. Extract the square root of 794%. 

1069. The pedestal of a certain monument is a cube 


1a 2) 


ig THE REGENTS’ QUESTIONS. 


ot granite, containing 373248 solid inches: what is the 
length of one of its sides? 


43 








1070. Express in words: 5000000750001. 

1071. If the product of two numbers is 346712, and 
one of the factors is 76, what is the other factor? 

1072. What is cancellation? 

1073. Find the least common multiple of 4, 14, 28, 
and 98. 

1074. The product of 3 numbers is $: two of the 
numbers are 24 and 4: what is the third? 

1075. What is the sum of six-millionths, four ten- 
thousandths, 19 hundred-thousandths, sixteen hun- 
dredths, and four tenths? 


1076. Reduce $ of 16.125 to a decimal fraction. 


1077. Make a receipted bill of the following articles 
as if sold to John Smith by yourself: 


16 ths. of tea,*at"$.85 ‘perib 2. 2o. FF See 
28 °° - ¢: coffee, at $254 perdb. 2. 24. Se 
15 yards of linen, at $.66 per yard.......... 


1078. How many acres are there in 250 city lots, es 
of which is 25 feet by 100? 

1079. Add 96 bu. 3 pk. 2 qt. 1 pt., 46 bu. 3 pk. 1 qt. 
1 pt., 2 pk. 1 qt. 1 pt., and 23 bu. 3 pk. 4 qt. 1 pt. 

1080. By the chronometer, it is 4 hr. 56 min. 4% 
sec., P. M., at Greenwich, when it is 12 mM. at New York; 
what is the longitude of New York? 

1081. 4 of 31s what part of =? 

1082. How many pounds of thread will it require to 


ARITHMETIC, "9 


make 60 yd. of 3 qr. wide, if 7 fb. make 14 yd. of 6 qr. 
wide? (Solve by double rule of three). 

1083. What is the difference between 54 per cent of 
$800, and 63 per cent of $1050? 

1084. If I sell a piano which cost $275, for $315, 
what is the rate per cent of gain? 

1085. What amount of government stock can I buy 
for $15525, when it sells at 35 per cent premium? 

1086. What is the simple interest of $3750.87, for 2 
years and 9 months, at 8 per cent? 

1087. The interest of $3675, for 3 years, is $771.75: 
- what is the rate? 

1088. What is the amount, at compound interest, of 
$250, for two years, at 8 per cent? 

1089. What is the bank discount of a note of $1000, 
payable in 60 days, at 6 per cent interest? 

1090. A man who has only $50, owes $75 to A, $150 
to B, and $100 to C: what should he pay to each? 

1091. Find the 4th power of 16. 

1092. What is the square root of 26883881? 

1093. How many small cubes, at 2 inches on a side, 
can be sawed out of a cube 2 feet on a side, if nothing 
is lost in sawing? 

1094. How many bricks, 8 inches long and 4 inches 
wide, will pave a yard that is 100 feet by 50 feet? 

1095. There was a company of soldiers, of whom 4 
were on guard, + preparing dinner, and the remainder, 
55 men, were drilling: how many were there in all? 

1096. A wall of 700 yards in length, was to be built 
in 29 days; 12 men were employed on it for 11 days, 
and only completed 220 yards: how many men must be 
added, to complete the wall in the required time? 


80 THE REGENTS’ QUESTIONS.. 


109%. If a house is 50 feet wide; and the post which 
supports the ridge-pole is 12 feet high, what will be the 
length of the rafters? 


} pai md 
1098. Copy and add: 


rem OAHHOreorwrowde@e 
ORNMARS-HNHOOnes 


PB 
1099. From— 
100200300400500600 take 908070605040302. 

1100. Divide 4500700424 by 407. 

1101. What is the value of 17 chests of tea, eacn con- 
taining 59 tbs., at $0.67 per tb? 

1102. For what is Troy weight used? 

1103. Give the table of Troy weight. 

1104. In 56 m. 7 fur. 37 rd. 12 ft. 9 in. now many 
inches? 

1105. How many cords in a pile of wood 15 ft. long, 
4 ft. wide, and 6} ft. high? 

1106. John Quincy Adams was oorn July 11, 1767, 
and died February 23, 1848. To what age did he live? 

1107. At £280 5s. 94d. for 97 tons of lead, what-is 
the cost per ton? 

1108. Find, by cancellation, the quotient of— 

8X5 xX3 X16 X 28divided by 10 X4X12X 4X7. 

1109. Find the last common multiple or dividend of 
9, 8, 12, 18, 24, 36 and 72. 

1110. Reduce #, 4, §, § to the least common denomi- 
nator. 

1111. How many cubic feet in 10 boxes, each 7? feet 
long, 1? ft. wide and 13 ft. high? 


ARITHMETIC, roll 


1142. If 3 of a saw-mill are worth $631.89, what 
are + of it worth? 

1113. Multiply eighty-seven thousandths by fifteen 
millionths. 

1114. What is the value of .965625 of a mile, in in- 
tegers of lower denominations? 

1115. What is § per cent of $1,728? 

1116, I have John Smith’s note for $144, dated J We 
25, 1879, payable on demand; how much will be due me, 
at 6 per cent simple interest, March 9, 1882? 

1117. What is the amount of $100 for 3 months, the 
interest to be added each month at 6 4? 

1118. What is the present worth of $477.71, due 4 
years hence, discounted at 6 per cent? 

1119. For what sum must a note at bank be made, 
payable in 3 months, at 6 per cent discount, to obtain 
$300 at the present time? 

1120. If I sell wood at $7.20 per cord, and gain 20 
per cent, what did it cost me per cord? 

1121. If 5 men can harvest a field in 12 hours, how 
many hours would it require if 4 more men were em- 
ployed? Solve by Rule of Three (Proportion. ) 

1122. If 15 oxen and 20 horses eat 6 tons of hay in 8 
weeks, how much will 12 oxen and 28 horses require in 
21 weeks? Solve by Double Rule of Three (Compound 
Proportion. ) 

1123. Find the square root of 9754.4376. 

1124. What must be the depth of a cubical cistern 
that will hold 3048.625 cubic feet of water? 

1125. How many tiles 8 in. square will cover a floor 
18 ft. long and 12 ft. wide? 


82 THE REGENTS’ QUESTIONS. 


stele bp te 


1126. Copy and add: 20570; 6206; 98.007; 63000; 
426.000626; 4287; 63.961; 102030; 405.0607; 8090; 
543.21; 1028848.414995. 

1127. Express by Arabic Notation: MDXCVDCCCLXIY. 

1128. Express by Roman Notation: 84796. 

1129. Numerate: 20567189.004321098. 

1130. Divide 31984875832 by 96813. 

1131. Find the value of 

(28—7) x 6+ (92--7) +9—(86+-10) +12. 

1132. Divide, using cancellation: 

15 X80 X27 X28 by 7xK20x8. | 

1133. Change 3, 44, #55, and ¢ to similar fractions 
having their least common denominator, and (1134) re- 
duce their sum to decimal form. 

1135. Find the greatest common divisor of 7955, 8769, 
6401. 

1136. How much must be paid for making 52 rd. 14 
ft. 8 in. of fence, at $.75 per foot? 

1137. A traveller, on reaching a certain place, found 
that his watch, which kept correct time for the place he 
left, was 2 hr. 22 mi. slower than the local time. Had 
he travelled eastward or westward, and how far, in cir- 
cular measure, had he come? 

1138. What per cent (expressed in words), of 30000 
bushels are 50 bushels? 

1139. What number diminished by 36% of itself = 
336? 

1140. What is the value of a lot 70 rd. long and 20 
rd. wide, at $47.25 per acre? 


ARITHMETIC. 83 


1141. A cistern has 3 pipes: The first will fill it in 
12 hours, the second in 16, and the third in 18 hours. 
If all run together, in what time will they fill it? (State 
this example as a proportion, if you can.) 

1142-43. What is the difference between simple inter- 
est on $328 for 2 yr. 7 mo. at 7%, and compound inter- 
est on same amount for same time, at 6%? 

1144. Find the balance due March 4 on a note dated 
January 1, 1879, for $580 at 5%, on which a payment of 
$85 has been made every 6 months,—using the U. 8. 
rule. 

1145. How much should be discounted on a bill of 
$3725.87, due in 8 mo. 10 da., if paid immediately, 
money being worth 5%? 

1146. Bought bonds at 115 and sold at 110, losing 
$300. How many bonds of $1000 each did I buy? 

1147. If A. puts in $4000 capital for 8 months, B. 
$6000 for 7 mo. and C. $3500 for 1 year, and they gain 
$2320, what is each partner’s share of the gain? 

1148. If 5 horses eat as much as 6 oxen, and 8 horses 
and 12 cattle eat 12 tons of hay in 40 days, how much 
hay will 7 horses and 15 oxen eat in 65 days? 

1149. Find the value of 7/.000238328. 

1150. A steamer goes due north at the rate of 15 
miles an hour, and another due west 18 miles an hour: 
how far apart will they be in 6 hours? 

1151. Find the cost, at 30 cts. per sq. yd., of plaster- 
ing the bottom and sides of a cubical cistern that will 
hold 300 barrels. 

1152. What is the area of a circle 5 ft. in diame- 
ter? 





84 THE REGENTS’ QUESTIONS. 


1153. What is the difference between 5 sq. ft. and & 
ft. square? Illustrate by a diagram. 


fe aad, Buseck 


1154. Write 1881 in characters of the Roman noe 
tation. 

1155. Write in words 73069294780069. 

1156. Copy and add: 


GQ ID S32 BO OS OH OD f= CO RCH 1D) DW Od &} BW CO 
mito +o 4+ HNnSEHDDSHSHSS 
ie.@) o> < (=P) 2“ 
1157. Define multiplication, multiplicand, multiplier, 


and product. 

1158. 330445150+3145=what number? 

1159. How could you obtain the dividend, the divisor, 
quotient and remainder being given?’ 

1160. Find the least common multiple of 15, 18, 
24, 35. 

1161. Add 8,4;, %, 32 and 43. 

1162. Bought 18 tb. of butter at 28} ct. per ib., giv- 
ing in return 224 lb. of lard at 12 ct. per fb., and the 
rest in cash; how much was the cash? 

1163. Write with figures: Ninety-three and six hun- 
hundred and nine ten-millionths. 

1164. On a railroad 149 mi, 234 rd. 4 yd. 2 ft. long, « 
there are 18 stations, including one at each end of the 
road. What is the average distance between stations? 

1165. How many boards 12 ft. long and 4 in. wide 
are required to floor a room which is 36 ft. by 27 ét.? 

1166. Find the difference in circular measure between 
Calcutta, E. Lon. 88° 19’ 2”., and Philadelphia, W. 
Lon. 75° 8’ 54’, 


ARITHMETIC, 85 


1167. Find the difference in time to correspond with 
your answer to Q. 1166. 

1168. Reduce 23444 sq. in. to a compound number. 

1169. What is the cost of %3590 tb. of coal, at $6.55 
per ton (2000 fb.)? 

1170. 3 tb. 13 oz. are what per cent of 9 Ib.? 

1171. Define per cent and percentage, as these terms 
are used in Arithmetic. 

1172. Find the simple interest on $740 for 1 yr. 5 
mo. 21 da., at 43 per cent? 

1173. What principal will amount to $310.60 in 3 yr. 
5 mo. 9 da., at 5 per cent simple interest? 

1174. What must be the face of a note for 90 days, at 
6 per cent, on which I can obtain at bank $472.86? 

1175. Two numbers are to each other as 7 to 11, and 
the greater is 329: what is the less? 

1176. Paid $2225 for 180 sheep and sold them for 
$2675: what should I gain on 1200 sheep at the same 
rate? (Solve by Proportion.) 

1177. If it cost $176 to hire 12 horses for 5 days, 
what will it cost to hire 10 horses for 18 days? (Solve 
by Compound Proportion. ) 

1178. How many miles of fence would be required to 
enclose 640 acres laid out as an exact square? 

1179. What is the cube root of 104329? 

1180. A person after spending 4 and } of his money 
and $20 more, had $80 left. What had he at first? 

1181. The width of a building being 38 ft., and the 
ridge of the roof 5 ft. higher than the eaves, how many 
feet of boards would be required to cover one of the | 
gable ends? 


86 THE REGENTS’ QUESTIONS. 


py 1 SE 


1182. Write in figures and numerate: Nine units of 
the 8th order, six of the 7th, three of the 5th, seven of 
the 4th, nine of the Ist. 

1183. Copy and numerate: 9004082501. 

1184. ( (256 x 25) —625)+35=? 

1185. Find the prime factors of 2310. 

1186. What is the greatest common divisor of 1313: 
and 4108? 

1187. What is the least common multiple of 84, 100, 
224 and 600? 

1188. If 2354 acres of land cost $47252, what will 628. 
acres cost, at the same rate? 

1189. From four hundred twenty-seven thousandths, 
take four hundred twenty-seven millionths. 

1190. Divide .125 by 8000. 

- 1191. Add six hundred and twenty-five thousandths;, 
four tenths; seven, and sixty-two ten-thousandths; 
three, and fifty-eight millionths; ninety-two, and seven. 
hundredths. 

1192. What is the cost of 18640 ft. of timber, at 
$4.50 per 100 ft. ? 

1193. How many cubic inches does the standard 
(wine) gallon contain? 1194. The standard bushel? 

1195. Reduce 41760 grains to pounds. 

1196. In 10 mi. 7 ch. 4 rd. 20 1., how many links? 

1197. Reduce 3 ot. 1 pt. 1 gi. to the decimal of a. 
gallon. . 

1198. How many shingles will it take to cover the 
roof of a building 46 feet long, each of the two sides 


ARITHMETIC, 87 


of the roof being 20 ft. wide, allowing each shingle to 
be 4 in. wide, and 5 in. of the length to be exposed to 
the weather? 


1199. What will it cost to build a wall 240 ft. long, 
6 ft. high, and 3 ft. thick, at $3.25 per 1000 bricks, the 
size of each brick being 8 in. x4 in. x2 in.? 

1200. If a note for $605.70 given June 20, 1878, on 
simple interest at 8 per cent, be taken up June 20, 1881, 
what amount will then be due, if no interest has been 
paid? 

1201. A man invests $2000 in bank stock, and re- 
ceives a semi-annual dividend of $75: what is the rate 
per cent of income, per annum? 

1202. Give the U. 8. rule for partial payments. 

1203. What is the present worth of a note for $1315- 
.389, due in 2 y. 6 mo., at 7 per cent? 

1204. If 6 men dig a cellar 22.5 ft. long, 17.3 ft. 
wide, and 10.25 ft. deep, in 2.5. days, of 12.3 ho., in 
how many days of 8.2 ho., can 9 men dig one 45 ft. 
long, 34.6 ft. wide, and 12.3 ft. deep? 

1205. If an army of 55225 be massed in a solid square, 
how many men will there be on a side? 

1206. A man bought a farm 198 rods long and 150 
rods wide, and agreed to give $32 an acre: how much 
did the farm cost him? 

1207. What is the length of one edge of a cistern of 
eubical form, containing 1331 solid feet? 

1208. How many barrels does such a cistern as the 
one described in the preceding question, contain? 

1209. Name and describe the stardard unit of weight 
in the Metric system. | 


88 THE REGENTS’ QUESTIONS. 


a Ora 


1210. Name five fundamental rules or operations of 
arithmetic. 

1211. What is a composite number? 

1212. Find the prime factors of 320. 

1213. What factors of two or more numbers must their 
greatest common divisor contain? 

1214. Find the greatest common divisor of 527 and 
1207. 

1215. What is the least common multiple of 24, 48, 
60 and 100? 

1216. What does the numerator of a fraction show? 

121%. What does the denominator show? 

1218. From 204 take 134. 

1219. If 5 barrels of flour cost $483, how many bar- 
rels can be bought for $2634? (Solve by analysis.) 

1220. Divide .00144 by 1.2. 

1221. How do you prove an example in division? 

1222. London is 77° 1’ east of Washington; what time 
is it at Washington when it is 12 M. at London? 

1223. What will 4 cwt. 3 qr. 15 tb. of sugar cost at 
$8.95 a cwt. (=100 ibs.) ? 

1224. A pile of wood is 6 ft. high, and 4 ft. wide: 
how long must it be to contain 10 cords? 

1225. How many acres in a rectangular field that is 
50 chains long and 30 chains wide? 

1226. What is 150 per cent of $560.25? 

1227. 47 is 20% of what number? 

1228. A wagon was sold for $329, which was 162% 
more than it cost: what did it cost? 


ARITHMETIC, | 89 


1229: If the interest of $36 for 3 yr. 8 mo. 19 da. is 
$8.034, what is the rate? 

1230. What is the bank discount on $120 for 120 days, 
at 7%? (Consider 360 days=1 year.) 

1231. What is the true discount on $120 for 120 days, 
at 7%? (Consider 360 days=1 year.) 

1232. If 2 of an acre of land is worth $148, how much 
is 18 of an acre worth? (Solve by proportion. ). 

1233. If 15 men in 9 days, by working 9 hours a day, 
build 36 rd. of stone-fence, how many rd. can 25 men 
build in 15 days, by working 8 hours a day? (Solve by 
compound proportion. ) 

1234. A. and B. entered into partnership: A. fur- 
nished $240 for 8 mo., and B. $559 for 5 mo. They 
lost $118: how much did each man lose? 

1235. In 25 kilogrammes how many pounds, Troy 
weight? (1 gramme=15.432 gr.) 

1236. What is the square root of 222784? 

1237. Give the method of proof for square root and 
prove answer to Q. 1236. 


ge 


1238. What is arithmetic? 

1239. What is a concrete or denominate number? 

1240. By what must I divide .7847 to get 1.9? 

1241. What kind of a number must a multiplier be? 

1242. What mixed number, multiplied by 254, will 
produce 54;°5? 

1243. What is a decimal fraction? 

1244. By how much does the cube of fifty-three hun- 
dredths exceed one millionth? 


90 THE REGENTS’ QUESTIONS. 


1245. Reduce 53%, 92, 43 to improper fractions, and 
then to their least common denominator. 

1246. Add the numbers in Q. 1245. 

1247. Reduce your answer to Q. 1246 to a whole num- 
ber and decimal (carrying the result to five decimal 
places). 

1248. If it requires 1 bu. 2 pk. of rye to sow an acre, 
how many quarts would be required for a rectangular 
field 484 ft. long by 270 ft. wide? 

1249. What is the druggist’s profit if he buys 5 tb. of 
opium at $12 per ib. avoirdupois, and sells it at $1 per 
oz. Troy? (7000 gr. = 1 tb. avoirdupois. ) 

* 1250. What would it cost to dig a cellar 30 ft. x 35 ft. 
x 8 ft., at $.84 per cubic yard? 

1251. The longitude of New York being 74° 0’ 3” W. 
and that of San Francisco being 122° 23’ W., what 
time is it at San Francisco when it is 1 P.M. at New 
York? 

1252. Reduce 12 miles to kilometers. (A meter = 
39.37 in.). 

1253. Into what pairs of factors may 12 be resolved? 

1254. What is the cost of 2 T. 15 ewt. (100 tbs.) 2 qr. 
15 tb. of hay, at ¢12.50 per T.? 

1255. Bought a hhd. of sugar for $55.75, and sold it 
at a profit of 124 per cent: what was the total profit? 

1256. What was the rate per cent of a tax for $52.88} . 
on property assessed at $3,525.50? oF 

1257. What is the discount, at 8 per cent, on a note 
for $750, payable without interest, in 2 yr. 3 mo. 20 da. ? 

1258. Find the proceeds of a note for $1,000, due-in 
90 days, discounted at bank at 6 per cent. 

1259. C. owes D. $900, of which $200 will be due in 


ARITHMETIC, ~ 9L 


3 mo., $300 in’6 mo., and the balance in 12 mo. What 
would be the mean or equated time of payment? 

1260. In the firm of A. & B., A invested $200 for 7 
mo. and B. $300 for 9 mo. They gained $125: what 
was each one’s share of the gain? 

1261. How many feet long is each side of a square 
acre? 

1262. If fifteen men can do a certain piece of work 
in-90 days of 10 hours each, in how many days of 12 
hours each can 20 men do the same work? 

1263. What is the premium on a building valued at. 
$3,000, insured for $ of its value, at 24 per cent? 

1264, Find the lacking term in the proportion: 

10 gal. 3 qt.: aos os 

1265. Find the length of the edge of a cubical box 

containing 262144 cu. ft. 





Bae EW (yee 


1266. What do you understand by the prime factors 
of a composite number? 

1267. Find the greatest common divisor of 360, 248, 
O72. 

1268. Find the least common multiple of 14, 16, 21, 
24, 112. 

1269, Exchanged a carriage worth $140, and five sets 
of harness worth $29 each, for 45 cords of wood and 
$73.50: what was the wood valued at, per cord? 

1270. Express the present year of the Christian era, 
by Roman notation. 

1271. Express in words: 645000021908. 

1272. Copy and numerate: 14627,5623. 


92 THE REGENTS’ QUESTIONS. 


1273. State the essential difference between common 
and decimal fractions. 

1274. Write the table of linear (or long) measure. | 

1275. A. owns 53; of a farm worth $15,422, and sells 
% of his rae ite the value of what he has left. 


1276. of © + 11t — what? 


6 | 6 

1277. (12515335182) divided by (8x14x9x 
5X17X20X6)=what? (Use cancellation. ) 

1278. Divide 87 fb. 8 oz. 19 pwt. 21 gr. by 7%, leaving 
the result in the same denominations. 

1279. Reduce .21675 T. to integers o. of lower de- 
nominations. 

1280. How many flagstones averaging 2 ft. long by 1 
ft. 3 in. wide will be at Ne for a walk 250 ft. long 
and 4 ft. 6 in. wide? 

1281. Find the side of a square field equivalent to a 
rectangular one 2859 yd. long and 714 yd. wide. 

1282. If a pile of wood 36 ft. long, 4 ft. wide and 5 
ft. high cost $58.50, what will a pile 60 ft. long, 4 ft. 
wide and 6 ft. high cost at the same rate? (Solve by 
proportion. ) 

Suppose that Jonas Smith owes you $343, for which 
he gives his promissory note of this date, payable to 
your order in 90 days, with legal interest, (1283) 
Write a complete copy of the note, and (1284) compute 
the amount payable when due, including three days 
grace. 

1285. How much can I realize on a note for $2144.50 
due in 3 mo. 10 da., discounted at bank at 8 per cent? 

1286. Bought 150 bbl. of flour at $6.75 per bbl., and 


bd 


ARITHMETIC, 93 


sold it at 123 per cent advance: what amoun did it. 
bring? 

1287. How long must $240 be on interest at 84 per 
cent to amount to $266.40? 

1288. A vessel and cargo are valued at $297000. 
The premium paid for insurance on $ of their value was: 
$2475. What was the rate of insurance? 

1289. What sum of money will amount to $228.60 in. 
2 yr. 4 mo. 18 da., at 6 per cent? 

1290. How many gallons in 24% hektoliters of vanes 
(A liter = 1.0567 qt.) ° 

1291. Explain the difference between specific and ad- 
valorem duties. 

1292. Extract the cube root of 50653. 


~ 


——THE SCHOOL BULLETIN PUBLICATIONS.—— 


Helps in Teaching Arithmetic, 


1. First Steps Among Figures. A drill book in the Fundamental Rules 
of Arithmetic. By Levi N. BEEBE. Cloth, 16mo, 3 editions. Pupils’ Hdition, 
pp. 140, 45 cts. Oral Edition, pp. 189, 50 cts. Teachers’ Edition, including ali 
in both the others, with additional parallel matter, Index, and Key, pp. 

00. 


fe 





—_— 


« '? . 


2. The Pestalozzian Series of Arithmetics. Teacher’s Manual and First- 
Year Text-Book for pupils in the first grade. Based upon Pestalozzi’s 
method of teaching Elementary Number. By Jamrs H. Hoosz. Boards, 
16mo, 2 editions. Pupils’ Edition, pp. 156, 35 cts. Teacher's Hdition, con- 
taining the former, with additional matter, pp. 217, 50 cts. 


3. The Word Method in Number. A series of 45 Cards, on which are 
‘printed all the possible Combinations of Two Figures. In box. By H. R. 
SANFORD. Size 3144x6inches. Price 50 cts. 


L. A Workin Number for Junior Classes in Graded Schools. By MARTHA 
Roe. Cloth, 16mo, pp. 116. Price 50cts. ° 


5. Intermediate Problems in Arithmetic for Junior Classes; containing 
more than 2,000 problems in Fractions, Reduction, and Decimals. By Emma 
A. WetcH. Cloth, 16mo, pp. 96. Price 50 cts. 


6. The Regents’ Questions in Arithmetic, being the 1293 questions given 
at the first 50 examinations held by the Regents of the University of the 
State of New York. Manilla, 16mo, pp. 98. 25 cts. Key, 25 cts. The same 
on Card-Board Slips, in Box, with Key, $1.00. 


7. Dime Question. Book, No. 18, Arithmetic. By ALBERT P. SouTHWICK 
Paper, 16mo, pp. 39. Price 10 cts. 


8. A Manual of Suggestions for Teaching Fractions, especially designed 
to accompany a Fractional Apparatus for developing the Idea of Fractions. 
_ By W. W. Davis. Paper, 16mo, pp. 43. Price 25 cts. Price of the Appa- 
ratus, net, $4.00. 


9. The 30 Possible Problems of Percentage, embracing a full and exhaust- 
‘ive discussion of the Theory of General Percentage, with 100 illustrative ex- 
amples. By W. H. BRapForp. Manilla, 16mo, pp. 34. Price 25 cts. 


10. Latitude and Longitude, and Longitude and Time. Embracing a 
comprehensive discussion, with over 100 illustrative questions and exam- 
ples. By J. A. Bassett. Manilla, 16mo, pp. 42. Price 25 cts. 


11, The International Date-Line,-or Where does the Day Begin? By 
Henry Couuins. Paper, 16mo, pp. 15. Price 15 cts. 


12, A Manual of Mensuration, for use in Common Schools and Acade- 
mies. By H. H. Hurron. Boards, 16mo, pp. 150. Price 50 cts. 


13. Number Lessons, somewhat after the Grubé Method, giving on one 
side the combinations of the digits, and on the other an unlimited series of 
drill-exercises. Heavy card-board, 10x11 inches. Price 10 ets. 


14. Age-Cards, containing 9 columns of figures, to determine a person’s 
age by adding the top numbers of those columns in which the number repre- 
senting the person’s age isfound. Heavy card-board, 4x6. Price 10 cts. 


15. Cube Root Blocks, carried to 3 places. Size 3inches, in box. $1.00, 


16. Numeral Frames, with 100 Colored Balls, $1.25; with 150 Colored 
Balls, $1.50. 


17. Algebra for Beginners. By O. S. MicuaEt. Cloth, 16mo, pp. 120. 
Price 75 cts. 


C. W. BARDEEN, Publisher, Syracuse, N. Y. 


——THE SCHOOL BULLETIN PUBLICATIONS.—— 


Helps in Regents’ Examinations, 


1. Regents’ Examination Paper. Six styles. 


For the Regents’ examinations we now prepare five forms of Examina- 
tion paper, all printed from new plates, and with some changes suggested 
by the board of Regents. 

PRICES PER REAM. 


Norr.—All the paper weighs fourteen pounds per ream of 480 full sheets 
of legal cap, but is put up in reams of 480 half sheets, weighing seven pounds. 
Please specify the letter, in ordering. NO ORDERS FILLED EXCEPT FOR 
EVEN REAMS. Even schools which have but two or three scholars to try 
will find it profitable to keep aream on hand. So much less attention as to 
the form of the paper is required of the scholar that he can give his undi- 
vided attention to answering the questions. It is now the practice of many 
of the best schools to put the scholars intending to try through one complete 
examination with questions given at a previous time, using this paper, and 
having all the formalities complied with. This gives the scholars confidence, 
and precludes the nervousness which is often fatal to success. 


B. All printed, for Arithmetic, Geography, or Grammar....... $2.25. 
C. All printed and numbered for Spelling...................... 2.50. 
D. 37 sheets Spelling, printed and numbered, , = 


185 sheets Arithmetic, Geography, Grammar, printed, 
258 sheets Arithmetic, Geography, Gram., not printed, 


480 sheets complete for 37 pupils, Rie oa ees 


The last form is preferred by nine-tenths of the schools, and we recom- 
mend it as the cheapest and most satisfactory. The sheets printed on the 
back are used only for the last sheet in each exercise, usually the second in 
Arithmetic and Geography, and the third in Grammar. 


E. The same as D. except that atu the sheets in Arithmetic, 
Grammar, and Geography are printed upon the back..... 2.40. 

F. All printed, for the Advanced Examinations only........... 2.25. 

G. All unprinted, suitable for any school examinations........ nly ay 


(= When five reams are ordered at one time, the name of the institution 
ordering will be printed on the back, if desired, without extra charge. 


2. Regents’ Examination Cards. A most convenient device for keeping 
a permanent record of the studies in which each pupil has passed. Manilla, 
544x7 in., per hundred, 50 cts. 


3. Regents’ Examination Record. Half-leather, folio, 9x14 in., in two 
sizes: a. 72 leaves, for 720 scholars, $2.00; 5. 144 leaves, for 1440 scholars, 
$2.50. 


Instead of loose cards, the Record gives on each page the record of five 
scholars, and is thus fitted for permanent reference. It is substantially 
bound, with title-page and alphabetical index. 


C. W. BARDEEN, Publisher, Syracuse, N. Y. 


—-THE SCHOOL BULLETIN PUBLICA TIONS,—— 


Helps in Teaching Literature. 


1, A Series of Questions in English and American Literature, prepared 
for class drill and private study by Mary F. Henprick, teacher in the State 
Normal School, Cortland, N. Y. 16mo, boards, pages 100, interleaved. 35cts. 


This edition is especially prepared for taking notes in the literature 
class, and may be used in connection with any text-book or under any in- 
struction. : 

2._ Early English Literature, from the Lay of Beowulf to Edmund Spen- 


ser. By Wm. B. Hartow, instructor in the High School, Syracuse, N. Y- 
16mo, cloth, pp. 138. 75 cts. 


This handsome volume gives copious extracts from all leading authors, 
of sufficient length to afford a fair taste of their style, while its biographical 
and critical notes give it rare value. 

3. Dime Question Book No, 2, General Literature, and No, 13, American 
Literature. By ALBERT P. SouTHwick. 16mo,.paper, pp. 35, 39. 10 cts. each. 

These are among the most interesting books in the series, abounding in 
allusion and suggestion, as well as giving full answers to every question. 
They afford a capital drill, and should be used in every class as a prepara- 
tion for examination. 

4. How to Obtain the Greatest Value from a Book. By the Rey. R. W. 
LowRrigz. 8vVvo, pp. 12. 25 cts. 

No one can read this essay without pleasure and profit. 

5. The Art of Questioning. By Josnua G. Fitcn. 16mo, paper, pp. 36. 
15 cts. 

Mr. Fitch, one of Her Majesty’s inspectors of schools, now recognized as 
the ablest of English writers on education, owed his early reputation to this 
address, the practical helpfulness of which is everywhere acknowledged. 

6. The Art of Securing Attention. By Josnua G. Fitcu. 16mo, paper, 
pp. 48. 15 cts. 

The Maryland School Journal well says: “It is itself an exemplification 
of the problem discussed, for the first page fixes the attention so that the 
reader never wearies, till he comes to the last and then wishes. that the end 
had not come so soon.”’ 

?. The Elocutionist’s Annual, comprising new and popular eaiees 
Recitations, Declamations, Dialogues, Tableaux. etc., etc. Compiled by 


payee J. W. SHOEMAKER. Paper, 16mo, pp. 200. 12 Numbers. Price of each, 
30 cts. . 


F Though primarily designed for classes in elocution, the character of the 
selections is so high that any of these volumes may be used with profit in a 
literature class. 


* ? The Bittle in the Public Schools, Paper, 24mo, 2 vols., pp. 214, 223. 
cts. 


These volumes contain the most important arguments, decisions, and 
addresses connected with the celebrated contest in Cincinnati, 1869. 


Cc. W. BARDEEN, Publisher, Syracuse, N. Y. 





‘ 


——THHE SCHOOL B ULLETIN PUBLICA TIONS.— 


‘Helps in Teaching Arithmetic. 


1. First Steps Among Figures. A drill book in thé Fundamental Rule 
of Arithmetic. By Levi N. BEEBE. Cloth, 16mo, 3 editions. Pupils’ dition 
pp. 140, 45 cts. Oral Hdition, pp. 139, 50 cts. Teachers’ Hdition, including all 
in both the others, with additional parallel matter, Index, and Key, pp. 
326, $1.00. 


2. The Pestalozzian Series of Arithmetics. Teacher’s Manual and First- 
Year Text-Book for pupils in the first grade. Based wpon Pestalozzi’s 
method of teaching Elementary Number. By JAmeEs H. Hoosz. Boards, 
16mo, 2 editions. Pupils’ Edition, pp. 156, 35 cts. Teachers dition, con- 
taining the former, with additional matter, pp. 217, 50 cts. 


3. The Word Method in. Number.. A series of 45’Cards, on which are 
printed all the possible Combinations of Two Figures. In box. By H. R. 
SANFORD. Size 344x6inches. Price 50 cts. 


4h. A Workin Number for Junior Classes in Graded Schools. By MARTHA 
Roz. Cloth, 16mo, pp. 116. Price 50 ct 


5. Intermediate Problems in Arithmetic for Junior Classes; containing 
more than 2,000 problems in Fractions, Reduction, and Decimals. By Emma 
A. Wetcx: Cloth, 16mo, pp. 96. Price 50 cts. 


6. The Regents’ Questions in Arithmetic, being the 1293 questions given 
at the first 50 examinations held by the Regents of the University of the 
State of New York. Manilla, 16mo, pp. 93. 25 cts. Key, 25 cts. The same 
on Card-Board Slips, in Box, with Key, $1.00. 


7. Dime Question Book, No. 18, Arithmetic. By ALBERT P. SoUTHWICK, 
Paper, 16mo, pp. 39. Price 10 cts. 


8. A Manual of Suggestions for Teaching Fractions, especially designed 
to accompany a Fractional Apparatus for developing the Idea of Fractions. 
By W. W. Davis. Paper, 16mo, pp. 43. Price 25 cts. Price of the Appa- 
ratus, net, $4.00. 


9. The 30 Possible Problems of Percentage, embracing a full and exhaust : 
ive discussion of the Theory of General Percentage, with 100 illustrative ex- 
amples. By W. H. Braprorp. Manilla, 16mo, pp. 34. Price 25 ets. 


‘10. Latitude and Longitude, and Longitude and Time. Embracing a 
comprehensive discussion, with over 100 illustrative questions and exam- 
ples, By J. A. Basserr. Manilla; 16mo, pp. 42. Price 25.cts. - 


11. The International Date-Line, or Where does the Day Begin? By 
Henry Couns. Paper, 16mo, pp. 15. Price 15 ets. 


12. A Manual of Mensuration, for use in Common Schools and Acade- 
mies. By H. H. Hurron. Boards, 16mo, pp. 150. Price 50 cts. 


13, Number Lessons, somewhat after the Grubé Method, giving on one 
side the combinations of the digits, and on the other an unlimited series of 
drill-exercises. Heavy card-board, 10x11 inches. Price 10 cts. 


th. Age-Cards, containing 9 columns of figures, to determine a person’s 
age by adding the top numbers of those columns in which the number repre- 
senting the person’s age is found. Heavy card-board, 4x6. Price 10 cts. 


15, Cube Root Blocks, carried to 3 places. Size 3inches, in box. $1.00. 


16. Numeral Frames, with 100 Colored Balls, $1.25; with 150 Colored 
Balls, $1.50. | 


17. Algebra for Beginners. By O. 8S. Micuaren. Cloth, 16mo, pp. 720. 
Price 75 cts. : 


C. W. BARDEEN, Publisher, Syracuse, N. Y. 


























ao) 


——THE SCHOOL P 


School Bulleti 


The School Agency has be 
for the best teachers and the b 
of place he is best fitted for, a1 
dozens of teachers on our list 
who want special work, superin. _ é A 
ness to a large city,—some surrounding Chuaeinee that they do not hy 
in their present location. We have scores who are giving entire satisfaction . 
where they are, and are paid as much as the community ean afford, but w mi, 
feel that they are capable of doing good work in a wider field and 
higher salary. We have others who are tolerably satisfied where they Le 
and who expect to stay, but who have encountered some opposition pga” 
board of yaaa plus and who want at gash to have opportunity to declu. - a 


tem can do toward bite saticiout DISCRIMINATION in the hiring of oe 
For years we have urged that this was all good teachers needed. Make 

- that only well-fitted teachers shall fill a certain place, and salary will t 
care of itself. Toward this our tales has nipnady done sorta 


wants to do, and if he is well- fitted aa will be patient he can get on 
tag? ig PS Pney, is trustworthy may be judged from: ine fact 


fitty randnehiens in New York normal, high, and union 
academies, besides more than 200 subordinate positions, E 
Alexander, Amenia Ac., Amsterdam Ac., Andover, ‘Kiae 
($2000), Baldwinsville, Belfast, Brasher Falls, Canandaigua Ac., Ca 
Champlain, Chittenango, Crown Point, Dunkirk, Fairfield Sem., 
Ac., Geddes, Greenville Ac., Heuvelton, Homer, Hudson, Hin ( 
Sem., Jasper, Manlius, Mannsyille, Mohawk, Moravia, Morrisville, 
Owego ($1500), Painted Post, Phoenix ($1500), Potsdam ($2800), Poug 
($1800), Rensselaerville Ac., Richfield Springs, St. Johnsville, Sala 
Sandy Creek, Saratoga Springs, Silver Creek, Ticonderoga, Warsa\ 
ingtonville, West Troy, Westport, Whitney’s Point, Yates Ac. 
Among positions in other States may be mentioned : e 
For men, Jersey City, $2600 and $2500; East Orange, N. J., $1000; e 
enworth, Ks., $2000; Ouray, Colo., $1000; New Orleans, La., $1000; 
_ For women, Marshalltown, Ia., $1000: St. Joseph, Mo., $850; Napa, Cal, 3005 = 
Ishpenning, Mich., $700; So. Norwalk, Ct., $650. Anioge places for women)” 
in New York, we may mention Buffalo Normal, $1200, Saratoga, $1 . 


If you want a better position, is it not fair to assume that your best 
by application to this Agency. For particulars, send stamp to — 


C. W. BARDEEN, Spree N 


